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.