Trip to Karachi

The previous winter we, a gathering of ten understudy, went to Karachi. Our montage had organized this visit. Our teacher. Mr.. Name Hosannas, was responsible for the gathering. We all had anticipated this visit. We had not seen Karachi, yet had gotten notification from individuals that it was a brilliant city. Specifically we were anxious to sue the sea. It was the 25th of December. At the point when we left Lahore via train. The excursion was long. The winter was more serious than expected. In any case, we were upbeat, and the long. Slow Journey didn't hose our cheerful dispositions. Next daddy arrived at Karachi late in the afternoon.We went draft to the boy troopers lodging on the new sovereigns street where we had organized to remain. One our way to the inn. We had our first perspective on Karachi. The absolute first thing we saw was that the street were extremely wide. The traffic was a lot more prominent than that we had found In Lahore. The quantity of vehicles we saw on the streets Indicated the success of the city. The structure were extremely palatial. On arriving at the lodging we felt tired. We chose to go through the night discreetly in our rooms. Following day, promptly toward the beginning of the day, we started our voyage through the city. Above all else we went to the Mazda of our adored pioneer, Squad ?I-Gamma , to pay our homage.After offering confidence we went to the house where Q help I-Gamma was conceived. It was an old there-story building. The room where our pioneer was conceived was on the primary floor. A portion of the furnishings and garments of Squad-I-Gamma were on the show In the room. After this we went to Clifton sea shore . The most well known cookout resort in Karachi There we saw the ocean just because. An incredible span of water was before us. It extended the extent that the eye could see. We stripped and not the ocean for a dip. Our educator was constantly advising us not to go extremely far. After the swim, we had tea I n a café the sea shore. It was currently mum for lunch.So we came back to the city. Subsequent to taking our lunch. We felt rather worn out and chose to rest to two or three house. At night we need out and wandered in the bazaar till late in the night. Each one appeared to be in a rush. The large lodgings of Karachi were impressive structures. They were lavishly finished. Brightly. It and loaded up with the hints of music and chuckling. Following day we visited Karachi port and house island. The maritime specialists compassionately permitted us to visit the PENS . Hardened , the officials and men of the boat were exceptionally polite. They gave all of us over the hip and disclosed all that we needed to know . N the night, we went to see the air terminal. The main Item on our developer for the following day was a visit to the state bank, it was a great structure. We were a lot of intrigued by its rooftop garden and elegantly designed meeting lobby and library. The rest day we spent in visiting the national historical center and the Karachi zoo, it was our shoot day in Karachi Trip to Karachi By Abductees Last winter we, a gathering of ten understudy, went to Karachi. Our collection had orchestrated 25th of December. At the point when we left Lahore via train. The Journey was long. The winter hose our cheerful moods. Following day we arrived at Karachi late in the afternoon.We went we had found in Lahore. The quantity of vehicles we saw on the streets showed the cherished pioneer, Squad - I-Gamma , to pay our tribute. In the wake of offering confidence we went to garments of Squad-I-Gamma were on the show in the room. After this we went to Clifton sea shore , the most well known outing resort in Karachi. There we saw the ocean for the first to go exceptionally far. After the swim, we had tea in a café the sea shore. It was presently time Karachi were mind blowing structures. They were lavishly designed. Brightly. It and air terminal. The main thing on our soft ware engineer for the following day was a visit to the state

9 Easy Tricks to Get Rid of Hiccups FAST

9 Easy Tricks to Get Rid of Hiccups FAST Ever recall being a part of an interesting conversation and all of a sudden hiccups begin? Or when youre about to give a weighty presentation and then the hics take over your speech?This can become very annoying. Most times this results in you trying out all sorts of creative and unusual tricks to get rid of them.It, therefore, is no surprise the abundance of hiccup remedies all over the web. However, this can be quite confusing as it becomes difficult to distinguish the working methods from mere fables.Nevertheless, in this article, you will see proven methods for getting rid of hiccups.Before we go ahead to the 9 tricks for hiccup relief, lets get to know a bit more about what exactly we want to get rid of.WHAT ARE HICCUPS? The National Organization for Rare Diseases (NORD) defines hiccups as an involuntary or uncontrolled spasmodic contraction of the muscle at the bottom of the lungs (diaphragm) which is followed by the quick closure of the vocal cords.Hiccups occur when your air intake is involuntarily obstructed and this can happen for absolutely no reason.Most times its a negligible nuisance, but when prolonged it can be indicative of very serious medical challenges.So basically when you have a hiccup what happens is that suddenly there is an involuntary contraction of your diaphragm alongside a contraction of your larynx or voice box as well as a complete closure of the glottis.All these things happen simultaneously and result in a rush of air into your lungs creating the annoying but familiar hic sound.HOW OFTEN DO HICCUPS APPEAR? Medically termed as synchronous diaphragmatic singultus or Flutter (SDF).Hiccups may occur in bouts or individually, and most times they are often rhythmic which means the time interval between each hic is quite consistent.Most times youd get hiccups from time to time and they can easily be resolved without treatment within a few minutes.However, in rare situations, you could experience chronic or prolonged hiccups, which coul d last up to a month or even more.These prolonged hiccups are known as intractable hiccups. Its important to state that if the bout persists for more than 48 hours, it is considered prolonged and you should meet a doctor.It could be a symptom of a very serious medical problem.A study carried out by Thomas Walsh on 99 people suffering from cancer of the esophagus showed that 27% of them experienced prolonged hiccups.Furthermore, according to another research, in relation to cancer of the esophagus, only 63% of people who are diagnosed in 6 months survive, whats more just 4% of people who are diagnosed after 5 years survive. Source: Pop CultureThis is why its vital to pay attention to prolonged hiccups and get medical help quickly.WHAT ARE THE CAUSES OF HICCUPS? The exact reason hiccups happens remains unclear; however, chronic hiccups are often associated with a broad range of medical challenges such as gastrointestinal problems, cancer, and stroke etc.Most hiccups get resolved without treatments but when prolonged they can lead to issues like depression and insomnia.Also staying away from alcohol and not eating too fast can assist in reducing the chance of getting hiccups.Now thats done with lets see 9 tricks to get rid of hiccups as quickly as they come!The traditional recommendations you may be used too like breathing into a paper bag or sipping water to get rid of hiccups rarely work. But the tricks below certainly will.1. Breathing Technique Inhale/Exhale and Diaphragm Movement This is a pretty easy technique to get rid of hiccups. Simply inhale through your mouth as many times as possible, then s wallow your saliva and restrict air from escaping out of your mouth.Take in air through your mouth and swallow saliva once again without letting air slip out.  Do this as much as you can. It could get very difficult the more you repeat it but do not desist.You will get to the point where you do not feel like its possible to swallow saliva anymore, push yourself and do it for the last time.Once you are certain that is impossible for you to repeat it again, then you can release air out of your nose. This will reset your breathing.If it still persists, you can proceed to the exhale step.You just need to take in as much air as you can and some more, then hold your breath.After you do this, start to let out the air you took in slowly while restricting some.You need to repeat this for as long as you can. Most times it takes 20 to 30 seconds to stop the hiccups.If youve got some really stubborn hiccups, however, you may need to do this; after inhaling and exhaling, take in a deep breath a nd keep it in.Then plug your ears and close your mouth (you could use your hands.)Now, all you need to do is move your diaphragm up and down and then exhale as soon as you feel the hiccups disappear. If the hiccups still persist repeat it again.2. Pressure Points Most people do not know that certain points on your body can stop hiccups immediately regardless of this ignorance though; pressure points are an efficient and effective way of getting rid of hiccups.As a matter of fact, a recent study showed that cancer patients who suffered from persistent or chronic hiccups saw a drastic reduction or total elimination of hiccups after undergoing acupuncture or pressure points techniques. Source: ResearchGateLets see some of these pressure points.a. PhiltrumThis is an easy one. Simply put your finger on the philtrum (the area between the middle of the top of your lip and the under of your nose.) Hold down on this spot as hard as you can and push it in towards your teeth.Keep the intensity of this pressure for approximately 30 seconds before you let go. This works often and it is especially useful for application on babies who usually have hiccups a lot.b. Sternum Pressure Point TechniqueFind your sternum. This is the bone at the center of your chest that links all your ribs together. Put your finger on the sternum and slowly move your fingers upwards till you locate its end point.Apply pressure on this bone for less than thirty seconds. Keep in mind that this does not have to be strong pressure, just strong enough for you to feel it and it should get rid of the hiccups.c. Under Your Collarbone TrickIn the hollow under your collarbone, right next to the breastbone put pressure on both sides for up to 10 seconds or till you feel the hiccup is gone. This is also helpful for asthma, chest congestion, and coughing.d. Pinky Finger This is a rather odd one but works like a charm, take the hand of your baby or yourself and apply hard pressure on the pinky fingernail surface for 10 seconds and the hiccups should cease immediately.e. Outer Chest Two inches right above the crease of the armpit about an inch inward and on the outer area of your chest, place hard pressure for between 20 to 30 minutes till you dont feel the hiccups anymore.This is also great in relieving breathing and coughing challenges.d. Under your Breastbone Find where your breastbone is (the long thin bone that links your right and left ribs.) Follow the bone downwards to its end where you can feel it gets hallow, then apply pressure with just your fingertip right there below the bone.Hold this for 20-30 seconds, or till you are certain the hiccups are gone.e. Hand Make a fist with your hand. This will reveal two vessels which we situated on your inner forearm. You would see a dent in your skin located very close to your wrist.All you need to do is to hold this point which is located between the two vessels and 3 fingers length towards the elbow and it should get rid of your hiccups.f. Abdomen This pressure point is located on your abdomen. For this simply find your belly button as well as your pubic bone. Now, at the center of these two spots is the presence of a pressure point that you can use to relieve hiccups.Its situated at the center of the line between the belly button and the pubic bone.For optimal effect, you need to lay down flat on your back and push on this spot for between 20 to 30 seconds and it will get rid of those annoying hics.3. Chew on a Piece of Lemon In 1981 a man by the name of Dr. Herman carried out a series of informal tests of a hiccup fix and he saw that he achieved a 88% success rate with his new found method.This method was discovered by bartenders who have been relying on this method for years to get rid of alcohol-induced hiccups.So, all you need to do is simply get a slice of lemon and cover it with some drops of Angostura bitters (keep in mind that it is alcoholic so this shouldnt be for kids) and then chew the lemon slice either leaving the rind or you can chew on it for some minutes.If its too sharp you can add sugar on it.The bitterness of the lemon and Angostura bitters will stimulate the lining of your gullet or the vagus nerve which relaxes your diaphragm.In addition to this, you can also drink vinegar or suck on a lemon some more if it persists.4. Rectal Massage Trick Even though this may seem outright impractical and bizarre, a rectal massage, using just one finger has been found to get rid of intractable hiccups. Now, you may ask why go to such a length for hiccups?Well, intractable hiccups usually last for more than a month and are tightly linked to underlying medical conditions.They disrupt eating, sleeping, socializing and can even ruin a patients social life. It may interest you to know that approximately 4,000 people in the USA get admitted to hospitals in relation to hiccups.With over 99% of individuals who are battling with intractable hiccups being men.In another study carried out, 7/7 patients were seen to be cured of hiccups by stimulation of the parasympathetic and sympathetic nerves.In one of the case studies a 60-year-old patient suffering from acute pancreatitis underwent a digital rectal massage, and after these hiccups left but returned back some hours later, he was able to easily terminate it immediately by undergoing another rectal massage.The research suggested that this technique should be considered in relation to intractable hiccups before you proceed to pharmacological agents.5. Drink Water from a Glass while Upside Down Another interesting remedy to get rid of hiccups is to drink water upside down from a glass. In order to be able to this accurately, bel ow are some steps to follow.First, place the far edge of the glass with water inside at the bottom of your upper lip. Secondly, bend forward and ensure that your upper lip is touching the outer tip of the glass of water.Thirdly, remain in the position (bent forward) and slowly pour the water from the glass into your mouth. As you do this the water will run over the upper palate of your mouth.Finally, swallow the water until you exhaust the water in the glass.After this is done wait for a few minutes to see if the hiccups have stopped if it doesnt stop you can repeat the process after a few more minutes.Although this is not a permanent solution for hiccups, it is a proven and tested temporary way of relieving yourself from the discomfort associated with hiccups.6. Swallow a Big Spoonful of Sugar You can get rid of hiccups by swallowing a spoonful of sugar. This is one of the most commonly prescribed and trusted home remedy for hiccups.A study carried out in the 1970s by scientists sh owed that 19 out of 20 patients with hiccups got rid of their hiccups by taking a spoonful of granulated sugar.Although there is no known definite reason why sugar stops hiccups, it is suggested that when the sugar is taken, the vagus nerve is stimulated, this vagus nerve connects the brain to the stomach and once it is stimulated by the sugar, it distracts the body.This makes the body forget about the hiccups and focuses on the sugar and when this is done the diaphragm spamming which manifests as hiccups are stopped.This is like distracting the body and giving it something order than the hiccup to focus on.Just like when your baby is crying and you give her a lollypop or her favorite toy or breast milk and the baby stops crying.The same is applicable to the brain when the body is having hiccups, once you take sugar; you create a distraction and a diversion from the hiccups to the sugar.Your brain then sends a signal to the rest of the body for the processing of the sugar and the di aphragm spamming is suspended for more important duties.Additionally, there is another school of thought that believes that the reason sugar stops hiccups is that sugar is a bit coarse and when it is being swallowed, the coarseness runs on the esophagus thereby irritating it and making the phrenic nerves to adjust themselves.Although this also Is not a proven fact, it doesnt eliminate the fact that sugar helps in stopping hiccups.7. Drinking Water As discomforting as hiccups can be, this home remedy isn’t complex at all. You can get rid of hiccups by simply drinking some water especially if it is not a severe hiccup case.Cold water is especially good for getting rid of hiccups when you take cold water; it helps to get rid of the irritation in the diaphragm which could be caused by various factors responsible for causing the hiccups.Once the irritation to the diaphragm is eliminated, the movement of the diaphragm will be restored back to the regular pattern.You can take about nine to ten quick sips of water from a glass in rapid succession.As you quickly gulp the water, the momentum which is caused by the contractions in the diaphragm is relaxed.The rhythmic contractions of the esophagus when drinking the water overrides the spasms of the diaphragm and this will cause the hiccups to subside and gradually stop.If the hiccups dont stop after the first round of gulps, you can repeat the process again after a few minutes, you will definitely get relieved after a short while.8. Stick out your TongueThis may be a bit gross so it is advisable not to do it in public so that you dont get people around you disgusted. You can get rid of hiccups by sticking out your tongue.Sticking out your tongue can stimulate the opening between the vocal cords and it is usually done by actors and singers but you too can do it.When you stick out your tongue the opening between the glottis is stimulated and you will breathe more smoothly this will eliminate the spasms that cause hiccup s.When you stick out your tongue, the vagus nerve will be stimulated and the diaphragm spasms will be eased, this will prevent the gag reflexes that cause hiccups.Alternatively, you can ease hiccups by pulling your tongue with your fingers. Just hold the end of your tongue and then tug. When you do this the vagus nerve will be stimulated and the diaphragm spasms will gradually subside thereby leading to the seizure of the hiccups.Ensure that your hands are clean before doing this. Dont put dirty hands into your mouth or on your tongue to avoid introducing harmful bacteria into your body which will cause illnesses that are more harmful than hiccups.9. Have a Spoonful of Peanut Butter Everyone loves a good peanut butter and jelly sandwich, and most people know how to whip one up but what you may not be aware of is the power of one of the sandwiches ingredients to get rid of hiccups.A large spoonful of peanut butter is a great way to eliminate those annoying hiccups. This happens due t o the process of chewing and removing it off your teeth and tongue.During the whole process, your breathing and swallowing patterns are interrupted which causes the hiccups to cease, as breathing and swallowing patterns are responsible for the hiccups in the first place.CONCLUSIONHiccups can be very annoying and at times signs of even greater health challenges, hence, they are certainly not something you can ignore especially if they do not disappear as magically as they came.They can impair the quality of your life in terms of eating, socialization, or even your work life. Imagine trying to carry out important assignments in your workplace while having hiccups, its a nightmare.This is why you need to stop it right into it’s a track as soon as it shows up.Also keep in mind that if your hiccups last for over 48 hours, you need to see a medical practitioner to ensure that it isnt as a result of a terminal disease and negligence could be extremely costly.Even though there are numerou s cases of prolonged hiccups which are connected to deadly diseases, do not get pensive when you get hiccups.Most times, it’s a simple hiccup that can be eliminated using very basic tricks.Regardless of how often youve tried all those funny and weird tricks online to get rid of hiccups, following the methods above which have been proven and tested you can rest assured of eliminating those hics once and for all.

A Mans Humility in the Grapes of Wrath by John Steinkbeck

A Man’s Humility In The Grapes of Wrath The Dust Bowl was a time in the 1930’s were malpractice cultivation, made cultivated farmland turn to dust then winds blew dust to make a huge dust storm that happened all over the U.S and Canadian prairies, it forced many to families to leave their homes and find jobs elsewhere. John Steinbeck is known for his skillfulness when it comes to detailing a situation or surrounding, he is the author of The Grapes of Wrath. In this excerpt from The Grapes of Wrath a man needs to feed his family with only ten cents to buy a loaf of bread, tries to persuade Mae; a waitress in a diner. Humility in this excerpt is shown as something a honorable and responsible person has. The man’s humility affects Mae’s behavior by keeping her away from being too defensive and being rude towards the man. In the beginning of the excerpt the man stands outside of the diner standing with curios humility. When Steinbeck uses â€Å"curious humility† curious means strange in this phrase , which means it was humility that is rare to see which makes it strange. In the first part of the excerpt the man comes up to the diner and asks if he can buy a loaf of bread for ten cents. â€Å"The man took off his dark, stained hat and stood with a curious humility in front of the screen. â€Å"Could you see your way to sell us a loaf of bread, ma’am?† Mae said, â€Å"This ain’t a grocery store. We got bread to make san’widges.† â€Å"I know, ma’am.† His humility was insistent. â€Å"We need bread and

Canadas Current Economic Situation - 1285 Words

An analysis of Canada s current economic situation depicts the nation to be under stress. Ottawa s current fiscal policy aims to operate under a budget deficit which has the potential to take several years before balancing itself. A balanced budget may take longer to achieve than expected should the government of Canada not raise taxes or cut national spending.(Blatchford) In chapters eleven and twelve of Dinner Party Economics, Evie Adomait and Richard Mantra investigate macroeconomic policies and how they pertain to the economy of our nation. It is critical to investigate political views and the differences in opinions between left wing and right wing ideologies regarding the economy. The results of these decisions and debates are what create the basis for Canada s overall macroeconomic policies. A study of macroeconomics allows one to understand the current situation of Canada s economy. In chapter 3 of Dinner Party economics, measures of life, liberty, and happiness are described by analyzing the macro economy. In the study of human happiness, three factors are known to contribute the happiness of people which includes demographic traits, economic factors, and political factors.(p. 18) Certain governments have separate policies regarding inflation and unemployment. These political factors are related to economic factors which can ultimately determine the happiness of the general population.(p. 20) Chapter 3 also describes how identifying catalysts of happiness isShow MoreRelatedAir Canadas Business Case Study1210 Words   |  5 Pagesregistered pension plans, supplemental pension plans and international pension plans. Air Canada’s pension funding obligations may vary significantly based on a wide variety of factors. Any changes to these factors may result in an increase in Air Canada’s obligations. 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Academic english Free Essays

The sociological imagination first coined by c. Wright mills in 1959 what is the sociological imagination? The vivid awareness of the relationship between personal experience and the wider society. -Seeing â€Å"strange in the familiar† is detaching yourself from individualistic interpretations of human behavior and accepting the initially â€Å"strange† notion that human behaviors are a product of social forces. We will write a custom essay sample on Academic english or any similar topic only for you Order Now The ability to see things socially and how things interact and influence each other that is the sociological imagination. How can we differentiate between personal troubles and social issues? Example: unemployment/ if your unemployed, that’s a trouble in your life (personal). But, if it was during the great recession, you were in the same boat as everybody else in society. Therefore your personal trouble is connected to a broader public issue. What is problem with the common sense explanations of ills? They fail to consider the wider picture of the issue yet they Just focus on pre- conceived Judgments for example in relation to aboriginal people a common sense explanation would be that they are all petrol sniffing no hoppers though this is not the case what has been failed to be realized here is that due to colonization indigenous people lost a lot of there rights and are still trying to recover from all they have lost in life. -Examples of social issues that might be better explained through investigating social forces and influences rather than individual failings Unemployed- its not necessarily that you’re lazy or don’t want to work. There are social forces at play that make it more likely some groups over others will be unemployed. Seeing the general in the particular show that age, gender, class, race, sexuality they all impact behaviors and life chances. Although we are individuals, social forces touch our lives in significant ways, even if we don’t see those forces. Sociology: is the study of society, whose goals are to establish, explain and predict patterned regularities of human behavior. The sociological imagination asks us to see the strange in the familiar and general in particular, linking our behaviors to broader social forces. Personal trouble re linked to broader public issues, and our goal in sociology is to uncover those links using the sociological data and not rely on common sense explanations Topic: social class and stratification -What is social stratification? Social stratification refers to a system of social inequality -Which societies experience social stratification? All societies have social stratification to some degree -Some societies have simpler stratification where they stratify along one dimension (such as age) while others are more complex and consist of many different factors reading stratification (such as age, race, gender, etc†¦ -3 types of stratification systems Estate systems Caste systems Class systems -definition of class in sociology the term class does not refer to one’s style or sophistication, rather social class is the social structural position groups hold relative to the economic, social, political and cultural resources of society. -class can not be directly observed but can be â€Å"seen† by observing the various displays others project such as brand of clothing, type of car, the places one shops. -these objects become symbols of an individuals lass status. Types of class systems: -Upper class: owns major share of corporate and personal wealth -Upper middle class: those with high incomes and high social prestige -Middle class: -Lower class: workers in skilled trades and low-income bureaucratic workers -Lower class: the displaced and poor. -The social class that you are in gives you different access to Jobs, income, education, power, and social status. Age, race, gender as well as class shape people’s experiences within society. -These differences allow different opportunities for success. How to cite Academic english, Papers

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Name: _________________________________________________________ Period: _____ APUSH: Mr. Svidron Chapter 8 - Varieties of American Nationalism : Study Guide Part I - A Growing Economy ( 216 - 219 ) Who were the leading exponents of the "national" over the "local" or "sectional" point of view that rose after the war? What factors contributed to the growth and development of this attitude? What were the programs proposed by the "nationalists" to deal with problems of currency and credit, "infant industries," and transportation? How were these separate programs linked together into a cohesive plan to develop America? What was the "internal improvements bill"? How did it fit into the nationalists" program, and what happened for it? Part II - Expanding Westward ( 219 - 22 2) What were the general characteristics of the westward movement after the War of 1812, and what geographical factors affected the decisions of where to settle? How did the advance of the southern frontier differ from the advance of settlement in the North? Describe the trade that developed between the western regions of North America and the United States early in the nineteenth century. Part III - The "Era of Good Feelings" ( 22 2 - 224 ) Why were the leaders of New England disturbed at the nomination and election of James Monroe for president, and what did Monroe do to quell their fears? Why did the United States want to annex Florida? How did the Adams-Onis negotiations resolve the issue? What were the causes of the Panic of 1819? What political and economic issues did the Panic raise? Part IV - The Downfall of the Federalists ( 22 4 - 22 8) What were the major elements of disagreement in the debate over the admission of Missouri into the Union? What was the Missouri Compromise? Why did nationalists regard it as a "happy resolution of a danger to the union?" Why were others less optimistic? What was the net effect of the opinions delivered by the Marshall Court? How did these opinions reflect John Marshall's philosophy of government? Who led the opposition to the Marshall Court, and what was the position they took in denouncing it? How did the case of Cohens v. Virginia answer these critics? What was the long-range significance of the case of Gibbons v. Ogden ? Of immediate importance, how did theis case help to blunt criticism of the Court? How were the nationalist inclinations of the Marshall Court visible in its decisions concerning the legal status of Indian tribes within the United States? How was it that the United States' proclamation of neutrality in the wars between Spain and its colonies actually aided the colonies? Why did the United States do this? What was the Monroe Doctrine? Why was it announced, and what was its significance? Part V - The Revival of Opposition ( 228 - 230) Why was the caucus system viewed with such disdain before the election of 1824? Who were the candidates in the election of 1824? What was the platform of each? What was the outcome of the election in 1824? How was that result arrived at, and what part did Henry Clay play in it? What was the "corrupt bargain," and why did it take place? What did John Quincy Adams plan to accomplish during his presidency? What role was the federal government to play in these plans? Was he successful? Why? What problems brought on the tariff debates of 1827 and 1828? In what way did the South respond to northeastern demands for a higher tariff, and on what did the anti-tariff forces base their stand? What was the outcome of these tariff debates, and why was it that few were pleased with these results? How had Andrew Jackson's supporters prepared for the election of 1828? What were the issues in the campaign, and what was the outcome? Who were the National Republicans? Who were their leaders? What programs did they support, and from what areas did they draw their strength? Part VI - Identification Identify each of the following, and explain why it is important within the context of the chapter. Second Bank of the U.S. "Infant Industries" Francis C. Lowell National Road Black Belt

Analyse a set of results and investigate the provided hypothesise Essays

Analyse a set of results and investigate the provided hypothesise Essays Analyse a set of results and investigate the provided hypothesise Essay Analyse a set of results and investigate the provided hypothesise Essay Essay Topic: Thesis My name is Khalil Sayed-Hossen, Im a year10 student and am carrying out the Guesstimate coursework task. For this coursework I am going to analyse a set of results and investigate the provided hypothesise. Plan Within the duration of producing this (Guestimate) coursework, I will first investigate the hypothesis given, that people estimate the length of lines better than the size of angles. Once I have done this I will begin to investigate hypothesise of my own. I will need to find away of proving and disproving these hypothesise through analysing relevant data. The data I will be using is from a pooled set of results that members of my class have collected and combined together to form a broad, clearer set of results. To be able to compare a set of results there must be a clear comparison. Since the results of the length of the line were given in the mm and the size of the angle in à ¯Ã‚ ¿Ã‚ ½ (degrees) there is no clear comparison. To be able to compare these two different types of data I will need to calculate the percentage error for each result. This is done by first calculating the differences between the actual size of the angle and the length of the line, i.e. errors, and then by using the formula: Error à ¯Ã‚ ¿Ã‚ ½ Correct à ¯Ã‚ ¿Ã‚ ½ 100 = percentage error Ways in which I can compare this data include, looking at the mean of the results, standard deviation and through producing scatter graphs. Scatter graphs are useful as, once the line of best fit has been drawn we can then analyse the inter-quartile range. I will also use any other methods that become apparent during the duration of this coursework and apply them when investigating my other hypothesis as well. During the course of my investigation I will try and eliminate any bias that might occur. This is most likely to happen when I select a range of data from the pool of results, when selecting specific data I will try and sample as many random data as I can and make sure that it hasnt all come from one person. Collection of data As part of this coursework, a given task was to collect data from random people by asking them to estimate the length of a line in (mm) and the size of an angle in (à ¯Ã‚ ¿Ã‚ ½) degrees. Once these results were taken they were then entered onto an X-cell spreadsheet as raw data. This was carried out by each member of the class, and once each of us had completed this task we pooled our results to give a broad, clearer set of data, which could be used to investigate any hypothesise. Data analysis Once all the data has been collected I will begin to make an analysis and apply it to the given hypothesise in the coursework, and also my own hypothesise. Before I can do this I need to change the data from being just raw data, to data I can compare. As said earlier, this can only be achieved by working out the percentage error for each data point for both line guesses and angle guesses. I will now work out the percentage errors. I will start by splitting investigation into different parts, depending on what methods Im using to prove or disprove the hypothesis of line. I will first select the data from the pool that I will use to analyse. This is not as simple as it sounds though. When selecting data from the pooled set of results we need to take into consideration how many males were asked and how many females were asked, this is called stratified random sampling. We do this to prevent any bias. For example, if our pooled set of results contained 40 males and 90 females and we then selected 20 males and 20 females results to analyse, our data would be bias, as the ratio of women to men or men to women would not be the same as the original set of results, and would have changed significant. Stratified random sampling prevents this, and is achieved in this case by taking the number of males and dividing that by the total number of people, and multiplying this figure by however many samples are needed, this will then give the correct ratio of women to men if the process is then repeated for the amount of women. The formula looks like this- Group (male or female) à ¯Ã‚ ¿Ã‚ ½ total à ¯Ã‚ ¿Ã‚ ½ preferred number of data points I will now use this method to select a set of data points from the pooled set of results. In total there are 167 males and females who estimated the line and the angle, of these, 85 were males and 82 were females. So through knowing this information we can now calculate how many results of men and women are needed in my sample of however many data points by using stratified random sampling. Stratified Random Sampling I want to sample forty angle data points from the total of 167. I will now attempt to do this using the stratified random sampling method and formula. Group (male or female) à ¯Ã‚ ¿Ã‚ ½ total à ¯Ã‚ ¿Ã‚ ½ preferred number of data points Males 85 à ¯Ã‚ ¿Ã‚ ½ 167 à ¯Ã‚ ¿Ã‚ ½ 40 = 20.35 *(say 20) Females 82 à ¯Ã‚ ¿Ã‚ ½ 167 à ¯Ã‚ ¿Ã‚ ½ 40 = 19.64 *(say 20) *Rounded to the nearest whole number to give exact amount needed. So from these results I can see that the ratio of males against females is equal when rounded to the nearest whole number. From gaining this information I can now accurately begin to specifically sample 40 random data points from the pooled set of results. My Sample data line angle age gender 1 2000 45 16 M 2 35 52 12 F 3 50 43 45 F 4 50 45 14 M 5 48 40 46 M 6 55 50 14 M 7 25 45 17 F 8 30 40 45 F 9 37.5 32 44 M 10 60 30 14 M 11 100 70 47 F 12 60 40 15 M 13 30 36 14 F 14 50 35 61 M 15 50 40 45 F 16 60 30 41 M 17 30 40 46 F 18 40 40 16 F 19 45 38 36 M 20 30 45 32 F 21 45 40 66 M 22 65 35 34 M 23 55 35 34 F 24 50 40 62 M 25 40 35 46 F 26 40 40 41 F 27 50 45 14 M 28 55 45 50 M 29 40 9 71 F 30 20 45 16 F 31 50 45 14 M 32 40 50 14 M 33 40 45 41 F 34 60 50 15 M 35 70 75 14 M 36 53.2 47.2 28 M 37 40 35 34 F 38 45 45 45 F 39 37 45 79 F 40 10 45 12 F When selecting the data not only did I have to take into account the ratio of males to females but I also have to consider the fact that each persons results may not be reliable, so to prevent this, my data selection was spread throughout the pool and not all from one section, this was another way of preventing bias and unreliable data. Once I had finished selecting my sample data. I noticed that within my set of selected data there was an outlier or anomaly, this I have highlighted in green. This anomaly must be removed and replaced as it is not a fair representation of the average guess of the length of the line, and when calculating the mean of line guesses, the anomaly would have a large weighted effect and would make the mean of the results insignificant and unreliable. Revised set of sample data line angle age gender 1 40 30 78 M 2 35 52 12 F 3 50 43 45 F 4 50 45 14 M 5 48 40 46 M 6 55 50 14 M 7 25 45 17 F 8 30 40 45 F 9 37.5 32 44 M 10 60 30 14 M 11 100 70 47 F 12 60 40 15 M 13 30 36 14 F 14 50 35 61 M 15 50 40 45 F 16 60 30 41 M 17 30 40 46 F 18 40 40 16 F 19 45 38 36 M 20 30 45 32 F 21 45 40 66 M 22 65 35 34 M 23 55 35 34 F 24 50 40 62 M 25 40 35 46 F 26 40 40 41 F 27 50 45 14 M 28 55 45 50 M 29 40 9 71 F 30 20 45 16 F 31 50 45 14 M 32 40 50 14 M 33 40 45 41 F 34 60 50 15 M 35 70 75 14 M 36 53.2 47.2 28 M 37 40 35 34 F 38 45 45 45 F 39 37 45 79 F 40 10 45 12 F This is set of sample data is going to be used through out my investigation of the length of the line. I will now begin my investigation. Firstly, I will begin by converting all the line and angle data points into their percentage errors. As said in my plan, this is done to implement a clear comparison. I will first need to work out all the errors of the data points. We do this by subtracting the just the original guesses from the correct length of the line and size of the angle. I will use Excel to help me with this as through the use of excel we can use simple formulas to work out equations. Testing the hypothesis The hypothesis states that people estimate the lengths of lines better than the size of angles. I will now test this hypothesis by calculating the mean and of both line results and angle results and compare them. Once I have done this I will then implement other methods, such as standard deviation cumulative frequency graph, and inter-quartile range. Comparing data As I mentioned earlier, we need to be able to compare the line an angle guesstimate data, but at the moment there is no comparison. To be able to compare this data we need to find a comparison. The best comparison is to work out the percentage errors for each line guesstimates, and angles guesstimates, as this is relevant to both the two different units of measure and will be easy to compare. First thoughts and assumptions I think from what I know about angles and lines that the hypothesis is wrong and that people will estimate the size of the angle more accurately. When considering the length of a line its difficult to know just how long it is, this is because an exact line length is difficult to visualise, whereas with an angle we know that 90 degrees is a right angle, 180 degrees is a half, and this we can picture in our minds. So when we see an angle we use the visualisations of sizes of angles that we know to be true to estimate the size of another angle, as they have to be either smaller or bigger than these. But when we try an estimate the length of a line its not so easy, as a line has no limitations, it can be as long as we want, but an angle can be no greater than 360 degrees. Also an angle is a fraction of a circle, but a line can be a fraction of a line than has an unimaginable greatness of length. So baring this in mind, when people estimate the size of the angle I think they will be closer to the correct size, than when they estimate the length of a line. Calculating the percentage errors for line guesstimates line age gender Line error Line percentage errors 1 40 78 M -5 -11.11111111 2 35 12 F -10 -22.22222222 3 50 45 F 5 11.11111111 4 50 14 M 5 11.11111111 5 48 46 M 3 6.666666667 6 55 14 M 10 22.22222222 7 25 17 F -20 -44.44444444 8 30 45 F -15 -33.33333333 9 37.5 44 M -7.5 -16.66666667 10 60 14 M 15 33.33333333 11 100 47 F 55 122.2222222 12 60 15 M 15 33.33333333 13 30 14 F -15 -33.33333333 14 50 61 M 5 11.11111111 15 50 45 F 5 11.11111111 16 60 41 M 15 33.33333333 17 30 46 F -15 -33.33333333 18 40 16 F -5 -11.11111111 19 45 36 M 0 0 20 30 32 F -15 -33.33333333 21 45 66 M 0 0 22 65 34 M 20 44.44444444 23 55 34 F 10 22.22222222 24 50 62 M 5 11.11111111 25 40 46 F -5 -11.11111111 26 40 41 F -5 -11.11111111 27 50 14 M 5 11.11111111 28 55 50 M 10 22.22222222 29 40 71 F -5 -11.11111111 30 20 16 F -25 -55.55555556 31 50 14 M 5 11.11111111 32 40 14 M -5 -11.11111111 33 40 41 F -5 -11.11111111 34 60 15 M 15 33.33333333 35 70 14 M 25 55.55555556 36 53.2 28 M 8.2 18.22222222 37 40 34 F -5 -11.11111111 38 45 45 F 0 0 39 37 79 F -8 -17.77777778 40 10 12 F -35 -77.77777778 I will start by investigating the line. I first calculated the errors, by subtracting the correct length of the line away from the guesses. Once I had calculated the errors I was then able to use the percentage error formula: Error à ¯Ã‚ ¿Ã‚ ½ Correct à ¯Ã‚ ¿Ã‚ ½ 100 = percentage error In excel we do this in the percentage error column by dividing the first data point in the line error column by 45, then by multiplying this by 100 to find the percentage. This found the percentage error for the first data point, to find the percentage error for all the other data points, because the formula is the same for each of the other data points in this column we simply highlight the first data point using the right click of the mouse, drag down and the formula works out the percentage error in each cell. Calculating the percentage error for angle guesstimates angle age gender Angle error Angle percentage errors (%) 1 30 78 M -6 -16.66666667 2 52 12 F 16 44.44444444 3 43 45 F 7 19.44444444 4 45 14 M 9 25 5 40 46 M 4 11.11111111 6 50 14 M 14 38.88888889 7 45 17 F 9 25 8 40 45 F 4 11.11111111 9 32 44 M -4 -11.11111111 10 30 14 M -6 -16.66666667 11 70 47 F 34 94.44444444 12 40 15 M 4 11.11111111 13 36 14 F 0 0 14 35 61 M -1 -2.777777778 15 40 45 F 4 11.11111111 16 30 41 M -6 -16.66666667 17 40 46 F 4 11.11111111 18 40 16 F 4 11.11111111 19 38 36 M 2 5.555555556 20 45 32 F 9 25 21 40 66 M 4 11.11111111 22 35 34 M -1 -2.777777778 23 35 34 F -1 -2.777777778 24 40 62 M 4 11.11111111 25 35 46 F -1 -2.777777778 26 40 41 F 4 11.11111111 27 45 14 M 9 25 28 45 50 M 9 25 29 9 71 F -27 -75 30 45 16 F 9 25 31 45 14 M 9 25 32 50 14 M 14 38.88888889 33 45 41 F 9 25 34 50 15 M 14 38.88888889 35 75 14 M 39 108.3333333 36 47.2 28 M 11.2 31.11111111 37 35 34 F -1 -2.777777778 38 45 45 F 9 25 39 45 79 F 9 25 40 45 12 F 9 25 When calculating the percentage error for the angle guesstimates, we repeat the same process needed to work out the percentage errors for the line guesstimates. Except in this case we divided the errors by 36, as this was the correct size of the angle. Now that I have calculated the percentage errors for all data points of line and angles within my sample data, I will be able to proceed with my fist method of proving or disproving the hypothesis, this will be by calculating the mean of line percentage errors and angle percentage errors. I will then compare both means. Calculating the mean of the line percentage errors Line percentage errors (%) 11.11111111 22.22222222 11.11111111 11.11111111 6.666666667 22.22222222 44.44444444 33.33333333 16.66666667 33.33333333 122.2222222 33.33333333 33.33333333 11.11111111 11.11111111 33.33333333 33.33333333 11.11111111 0 33.33333333 0 44.44444444 22.22222222 11.11111111 11.11111111 11.11111111 11.11111111 22.22222222 11.11111111 55.55555556 11.11111111 11.11111111 11.11111111 33.33333333 55.55555556 18.22222222 11.11111111 0 17.77777778 77.77777778 Line percentage errors (%) -11.11111111 -22.22222222 11.11111111 11.11111111 6.666666667 22.22222222 -44.44444444 -33.33333333 -16.66666667 33.33333333 122.2222222 33.33333333 -33.33333333 11.11111111 11.11111111 33.33333333 -33.33333333 -11.11111111 0 -33.33333333 0 44.44444444 22.22222222 11.11111111 -11.11111111 -11.11111111 11.11111111 22.22222222 -11.11111111 -55.55555556 11.11111111 -11.11111111 -11.11111111 33.33333333 55.55555556 18.22222222 -11.11111111 0 -17.77777778 -77.77777778 To calculate the mean percentage error, we need to use the usual method of calculating any mean result. We need to add up all the percentage error data points and divide by how many data points there are. But before we can do this we need to make any negative percentage error data points positive. If this is not done, when we add up all the data, the negative data will subtract itself from any positive data, and this we do not want, as we are only looking at the percentage of which they were away from the correct, weather or not the guess was too high or too low, is insignificant. Adding all percentage errors To add the percentage errors we need to convert the negatives into positives, as said earlier. I did this in excel by squaring each negative percentage, by using the formula ^2, and then square rooting each percentage. Once I had done this I was able to add up all the percentage errors by first highlighting all the data points in the percentage error column and then by using the formula ? in excel, which means the sum of. This gave me the sum of all the percentage errors for the line, and the angle. The sum of the percentage errors for the line was 981.5555556% and for the angles 795%. Line percentage errors (%) Angle percentage errors (%) 11.11111111 16.66666667 22.22222222 44.44444444 11.11111111 19.44444444 11.11111111 25 6.666666667 11.11111111 22.22222222 38.88888889 44.44444444 25 33.33333333 11.11111111 16.66666667 11.11111111 33.33333333 16.66666667 122.2222222 94.44444444 33.33333333 11.11111111 33.33333333 0 11.11111111 2.777777778 11.11111111 11.11111111 33.33333333 16.66666667 33.33333333 11.11111111 11.11111111 11.11111111 0 5.555555556 33.33333333 25 0 11.11111111 44.44444444 2.777777778 22.22222222 2.777777778 11.11111111 11.11111111 11.11111111 2.777777778 11.11111111 11.11111111 11.11111111 25 22.22222222 25 11.11111111 75 55.55555556 25 11.11111111 25 11.11111111 38.88888889 11.11111111 25 33.33333333 38.88888889 55.55555556 108.3333333 18.22222222 31.11111111 11.11111111 2.777777778 0 25 17.77777778 25 77.77777778 25 24.53888889 23.625 Finding the mean percentage error What I did next was divide both numbers by 40, as this was the amount of data points. I was left with the products, 24.53888889% for the line, and 23.625% for the angles, which were the mean percentage errors. These are highlighted in yellow. The hypothesis states that people estimate lines better than angles. From information I have gathered through calculating the mean result of the percentage errors I have found that my findings contradict the hypothesis, and that people tend to estimate the size of angles better than the length of lines. My assumption that people will estimate the size of the angle better than the length of the line, for reasons mentioned earlier, was found to be true through this investigation. If I were able to make these findings more reliable I would have sampled a larger amount of data from a more extensive pool of data, as this would have decreased the effect that unreliable, bias data had on the mean. I will now investigate through other methods of proving and disproving the hypothesis. Cumulative frequency I could have at this point produced a frequency graph, but due to limitation in time I have decided to produce a cumulative frequency graph as this is a clearer, indicative representation of data, and I will be able to deduce more information from it. If we represent the percentage errors of both line and angle percentage errors individually in frequency tables, we can calculate cumulative frequencies. Once we have done this we can use these new values, when plotted and on a graph, to form a cumulative frequency curve. This is useful as we will be able to find the median from the halfway point, and we will be able to locate the upper and lower quartiles. The upper quartile is 75% and the lower quartile is 25 %. From knowing the upper and lower quartile, we can calculate the inter-quartile range. This is found by subtracting the lower quartile from the upper quartile. The inter quartile range is half of the data distribution and shows how widely spread the data is, if the inter-quartile range is small, then the distribution is bunched together and shows more consistent results, if the inter-quartile range is large, then the distribution is spread and shows a wider variation in results. We can compare both the line inter-quartile range and the angle inter-quartile range, and whichever is smallest, will be the most accurate, as this would mean a smaller percentage error. Line percentage errors cumulative frequency table Line percentage errors (%) Frequency cumulative frequency upper limits 0.-10 4 4 ? 10 11-.20 17 21 ? 20 21-30 5 26 ? 30 31-40 8 34 ? 40 41-50 2 36 ? 50 51-60 2 38 ? 60 61-70 0 38 ? 70 71-80 1 39 ? 80 81-90 0 39 ? 90 91-100 0 39 ? 100 101-110 0 39 ? 110 111-120 0 39 ? 120 121-130 1 40 ? 130 To produce a cumulative frequency table, you first set the boundaries for each group of percentage errors this has been done in the first column. We then count all the percentages that are within the boundaries of that group, and this is then recorded in the frequency column. Once this has been done for each group, we can then calculate the cumulative frequency by adding each of the previous frequency data points to the next, and record each product in the cumulative frequency column. We then state in the in the upper limits column, what the highest percentage error can be. Now that I have produced a cumulative frequency table, I can now start to produce a cumulative frequency graph. Line percentage errors cumulative frequency graph The graph shows the cumulative frequency curve of the line percentage errors. From this curve I can find the lower and upper quartiles. These were; Lower quartile = 13% Upper quartile = 35% From knowing the lower and upper quartiles, I can calculate the inter-quartile range, by simply subtracting the lower quartile from the upper quartile. Inter-quartile range = (35 13) % = 22% The inter-quartile range of the line percentage error, cumulative frequency graph is 22%. I will now investigate the cumulative frequency graph, of the angle percentage error. Angle percentage errors cumulative frequency table Angle percentage errors (%) Frequency cumulative frequency upper limits 010 7 7 ? 10 1120 14 21 ? 20 2130 11 32 ? 30 3140 4 36 ? 40 4150 1 37 ? 50 5160 0 37 ? 60 6170 0 37 ? 70 7180 1 38 ? 80 8190 0 38 ? 90 91100 1 39 ? 100 101110 1 40 ? 110 111120 0 40 ? 120 121130 0 40 ? 130 I have produced the cumulative frequency table for the angle percentage errors. I can now begin to draw the cumulative frequency graph. Once I have drawn this I will calculate the lower and upper quartiles, and then calculate the inter-quartile range. Once I know the inter-quartile range I will be able to compare the inter-quartile range for the line data and the inter-quartile range for the angle data Angle percentage errors cumulative frequency graph The graph shows the cumulative frequency curve of the angle percentage errors. From this curve I can find the lower and upper quartiles. These were; Lower quartile = 12% Upper quartile = 28% From knowing the lower and upper quartiles, I can calculate the inter-quartile range, by simply subtracting the lower quartile from the upper quartile as I did for the line percentage cumulative quartiles. Inter-quartile range = (28 12) % = 16% Comparing graph data I have found the inter-quartile range of both line and angle cumulative frequency graphs. Theses were, for the line percentage errors- 22%, and for the angle percentage errors-16%. Its clear to see from these results that the inter-quartile range of the angle percentage errors was much less than the inter-quartile ranges of the line percentage errors. There is a difference of 6% percent between the two results. This shows that there was a wider spread of data for the line percentage errors, and that the accuracy when estimating the lines length was not as precise as when the angles were estimated. I have shown through my investigations that when people estimated the length of a line and the size of an angle, results were more accurate when the size of the angle was estimated. My first thoughts were that people would estimate the size of angles better, as angles are a fraction of a circle, which is limited. But the length of a line is un-limited and it is difficult to visualise the correct length of lines. I believe that my thoughts could be true as the mean and inter-quartile range of the angle percentage errors, were more accurate than the line on both occasions. I have investigated this hypothesis using two different methods, and through them have concluded that people estimate the length of angles more accurately. My findings contradict the given hypothesis. Now that I have finished investigating the given hypothesis, I will begin to investigate my own hypothesis. Hypothesis 2 Females estimate the length of lines and size of angles better than males The above hypothesis is a hypothesis of my own and is one which I will now begin to investigate. I will use the same method of comparing percentage errors as used in the previous investigation. First thoughts Without analysing the comparisons between the results given from the different sexes, its difficult to say weather or not females were more accurate, as at first glance, it is not obvious. Data analysis To be able to compare male and female estimates, I must first divide my sampled data into two sections, one section of male estimates and another section of female estimates. Earlier in my investigation I specifically selected 20 male data points and 20 female data points using Stratified random sampling, to eliminate bias. This is now useful to me as than there is an equal amount of female and male data points, so I will be able to use an analyse my original set of sampled data. I will now separate male and females guesses into two columns and compare the mean of the percentage errors. I will be able to mix line and angle percentage errors as I am comparing how females and males estimate lines and angles generally and not line and angles individually. Male Line and Angle percentage errors Line and Angle percentage errors (%) 1 11.11111 2 4.444444 3 6.666667 4 8.888889 5 11.11111 6 13.33333 7 15.55556 8 17.77778 9 20 10 22.22222 11 24.44444 12 26.66667 13 28.88889 14 31.11111 15 33.33333 16 35.55556 17 37.77778 18 40 19 42.22222 20 44.44444 21 16.66667 22 25 23 11.11111 24 38.88889 25 11.11111 26 16.66667 27 11.11111 28 2.777778 29 16.66667 30 5.555556 31 11.11111 32 2.777778 33 11.11111 34 25 35 25 36 25 37 38.88889 38 38.88889 39 108.3333 40 31.11111 ?=948.3333 To calculate the mean percentage error I first need to add up all the percentage errors. To do this, I will use the ? formula in excel, as used earlier. The number highlighted in green is the sums of the line and the angle percentage errors. To gain the mean of the percentage I need to divide them by 40, as this is the amount of percentage error data points. The product I am left with is 23.70833% this is the mean percentage error for male line and angle estimates. Female Line and Angle percentage errors Line and angle percentage errors (%) 1 22.22222 2 11.11111 3 44.44444 4 33.33333 5 122.2222 6 33.33333 7 11.11111 8 33.33333 9 11.11111 10 33.33333 11 22.22222 12 11.11111 13 11.11111 14 11.11111 15 55.55556 16 11.11111 17 11.11111 18 0 19 17.77778 20 77.77778 21 44.44444 22 19.44444 23 25 24 11.11111 25 94.44444 26 0 27 11.11111 28 11.11111 29 11.11111 30 25 31 2.777778 32 2.777778 33 11.11111 34 75 35 25 36 25 37 2.777778 38 25 39 25 40 25 26.41667 If I repeat the same process used for the male percentage errors, to obtain the mean of the female percentage errors, I am left with the product 26.41667%. This is the mean percentage error for line and angle percentage errors. From calculating the mean percentage errors of line and angle percentage errors, for both genders, I have found that males were more accurate at estimating the size angles and length of lines than females, and that this contradicts my hypothesis. To improve the reliability of my findings I will now investigate standard deviation. Standard deviation Standard deviation is useful to measure the spread of the data. Standard deviation gives a more detailed picture of the way in which data is dispersed around the mean, being the centre of distribution. If the difference between the standard deviation and the mean is large, the data is not consistent and is not typical of the mean. To work the standard deviation, I need to subtract the mean percentage error from each percentage error to create a set of deviations. Once I have done this I need to square each deviation to make a set of squared deviations. I can place this information in a table x (x-x) (x-x)à ¯Ã‚ ¿Ã‚ ½ x = percentage error x = mean percentage error I then need to average the set of deviations, by finding the mean of the standard deviations. Once I have done this I will need to take the square root so that the answer is back to the original measure, in this case percentage. This can be represented by the formula V ?(x x) à ¯Ã‚ ¿Ã‚ ½ à ¯Ã‚ ¿Ã‚ ½ n I will now use my male sample percentage error data, to formulate a table Standard deviation table of male percentage errors x (x-x) (x-x)à ¯Ã‚ ¿Ã‚ ½ 2.777778 -20.9306 438.08801 2.777778 -20.9306 438.08801 4.444444 -19.2639 371.0973 5.555556 -18.1528 329.5232 6.666667 -17.0417 290.41828 8.888889 -14.8194 219.61583 11.11111 -12.5972 158.68995 11.11111 -12.5972 158.68995 11.11111 -12.5972 158.68995 11.11111 -12.5972 158.68995 11.11111 -12.5972 158.68995 11.11111 -12.5972 158.68995 11.11111 -12.5972 158.68995 13.33333 -10.375 107.64063 15.55556 -8.15277 66.467659 16.66667 -7.04166 49.584976 16.66667 -7.04166 49.584976 16.66667 -7.04166 49.584976 17.77778 -5.93055 35.171423 20 -3.70833 13.751711 22.22222 -1.48611 2.2085229 24.44444 0.73611 0.5418579 25 1.29167 1.6684114 25 1.29167 1.6684114 25 1.29167 1.6684114 25 1.29167 1.6684114 26.66667 2.95834 8.7517756 28.88889 5.18056 26.838202 31.11111 7.40278 54.801152 31.11111 7.40278 54.801152 33.33333 9.625 92.640625 35.55556 11.84723 140.35686 37.77778 14.06945 197.94942 38.88889 15.18056 230.4494 38.88889 15.18056 230.4494 38.88889 15.18056 230.4494 40 16.29167 265.41851 42.22222 18.51389 342.76412 44.44444 20.73611 429.98626 108.3333 84.62497 7161.3855 13045.912 326.14781 18.059563 Once I had organized the data from smallest to largest in column x, I could calculate column 2(x-x) by subtracting the mean, which is 23.70833, from each percentage error. I then calculated column three (x-x) à ¯Ã‚ ¿Ã‚ ½ by multiplying each data point in column two by power 2, by using the excel formula ^2. Calculating the Standard Deviation Once I had finished formulating the table, I was able to find the Standard Deviation. I need to use the formula V ?(x x) à ¯Ã‚ ¿Ã‚ ½ à ¯Ã‚ ¿Ã‚ ½ n. So I firstly had to work out the sum of the (x-x) à ¯Ã‚ ¿Ã‚ ½ column, the product was 13045.912. I then divided this number by 40, to find the mean of the data, as this is the number of data points and the product was 326.14781.The final calculation I had to make to conclude with the standard deviation was to square root the mean, as I needed to find the original unit of measure, in this case it was percentage. The standard deviation of the male line and angle estimates is 18.1% to 3.sf. Standard deviation table of female percentage errors x (x-x) (x-x)à ¯Ã‚ ¿Ã‚ ½ 0 -26.4167 697.84045 0 -26.4167 697.84045 2.777778 -23.6389 558.79721 2.777778 -23.6389 558.79721 2.777778 -23.6389 558.79721 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 11.11111 -15.3056 234.26017 17.77778 -8.63889 74.63042 19.44444 -6.97223 48.611991 22.22222 -4.19445 17.593411 22.22222 -4.19445 17.593411 25 -1.41667 2.0069539 25 -1.41667 2.0069539 25 -1.41667 2.0069539 25 -1.41667 2.0069539 25 -1.41667 2.0069539 25 -1.41667 2.0069539 25 -1.41667 2.0069539 33.33333 6.91666 47.840186 33.33333 6.91666 47.840186 33.33333 6.91666 47.840186 33.33333 6.91666 47.840186 44.44444 18.02777 325.00049 44.44444 18.02777 325.00049 55.55556 29.13889 849.07491 75 48.58333 2360.34 77.77778 51.36111 2637.9636 94.44444 68.02777 4627.7775 122.2222 95.80553 9178.6996 26785.15 669.62875 25.877186 Once I had organized the data from smallest to largest in column x, I could calculate column 2(x-x) by subtracting the mean, which is 26.41667 from each percentage error. I then calculated column three (x-x) à ¯Ã‚ ¿Ã‚ ½ by multiplying each data point in column two by power 2, by using the excel formula ^2. Calculating the Standard Deviation Once I had finished formulating the table, I was able to find the Standard Deviation. I needed to use the formula V ?(x x) à ¯Ã‚ ¿Ã‚ ½ à ¯Ã‚ ¿Ã‚ ½ n. So I firstly had to work out the sum of the (x-x) à ¯Ã‚ ¿Ã‚ ½ column, the product was 13045.912. I then divided this number by 40, to find the mean of the data, as this is the number of data points and the product was 326.14781.The final calculation I had to make to conclude with the standard deviation was to square root the mean, as I needed to find the original unit of measure, in this case it was percentage. The standard deviation of the male line and angle estimates is 25.8% to 3.sf. Comparing data From investigating my hypothesis, I have found that through investigating the mean of the percentage errors for male and female estimates, males were more accurate. But when I investigated the percentage errors through standard deviation, I found that females were more consistent with estimating and that female estimates were more typical of the mean than male estimates. But this is irrelevant as the data still shows that males were more accurate as the standard deviation of the male estimates was 18.1% and the standard deviation of female estimates was 25.8%, which is a difference of 7.7%. My findings contradict my hypothesis and males were more accurate at estimating lengths of lines and size of angles. Evaluation I believe that I have investigated both hypotheses as much as I could have in the time I have been given. The conclusions I have come to through my findings were based upon the data pooled by my class. I believe that some of this data may have been unreliable due to errors etc. I believe that with a more extensive pool of data, my findings would have been more conclusive an indicative a true representation. I have reached the end of my investigation. If the time allocation was greater, I could have investigated another hypothesis such as Younger people estimate lines and angles better than older people.