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"Estimation improves with age".

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Introduction

Statistics Coursework For this piece of statistical coursework I have been asked to analyse date using a range of statistical distributors and measures. My hypothesis for the investigation is related to estimation, the hypothesis being: "Estimation improves with age" I have been given a set of a line and angle measuring and 50o. Using the data given to me for this investigation I am going to find the mode, mean and median from the inter-quartile range. I must do this for each specific group, both child and adult. I will do this because I will be able to compare all of my results. I will then see if those who are older have better results than children to check to see if my hypothesis is correct. I believe we were given the sizes of the angle and length for these reasons. Small lengths are within our grasp as estimations. Smaller lines are simpler for us to see and predict more accurate measurements. As the angle is between 0o and 90o meaning we have estimation is our minds as we have to angles to base our prediction between. To test this hypothesis I am going to use a range of statistical measures in relation to the provided data. I will calculate the averages and the range to see if they support this claim or not. I will then display the data in different ways to see what other information I can gain from it. Length of Line (mm) Angle Size (degrees) Children Adults Children Adults Total Freq 40 30 40 30 Mean (x) 50.6mm 49.2mm 49.3 49.1 % Error 5 2.7 5 1.8 Mode 50mm 50mm 45 / 52 46 % Error 4 4 10 8 Median 50mm 51mm 49.5 49 % Error 4 6.25 1 2 Range 40 23 33 26 But this data is limited in its use. It tells us very little in regards to our hypothesis, as the results are very similar. ...read more.

Middle

Adult Estimation of the Angle: Positive Result: This time the adults estimations were very close to the actual answer, the bulge was huge around the answer showing that they were better at estimating the angle. Overall, looking at my stem and leaf diagrams I have noticed that they all have a consistent shape. The majority of the leafs were situated around the 40's and the 50's. This means that the estimate we around 40-59. This shows that the majority of the answer we near enough the actual answers. This could account for the earlier results showing the children and adults were similar in their prediction, as they are both quite close. In the children's estimation of the line I can see that it has positive correlation. estimation range is from 30 to 70. I can tell by looking at the numbers that I have highlighted that two children were successful in estimating the actual answer. In the adults estimation of the line estimation range is from 35 and 67. I can see that only one adult was successful in estimating the actual length. From this piece of evidence the hypothesis isn't supported because the children have estimated correctly more than the adults. In the children's estimation of the size of the angle I can see that it has positive correlation. The estimation range is 32 to 65. I can tell by looking at the numbers that I have highlighted that two children were successful in estimating the actual answer. In the adults estimation of the line estimation range is from 33 and 59. I can see that only one adult was successful in estimating the actual size of the angle. From this piece of evidence the hypothesis is neither supported or hindered as both adult and child scored equally well. So from my stem and leaf diagrams the hypothesis isn't supported wholly as the majority of the better estimations were by the children. ...read more.

Conclusion

Also I will produce cumulative frequency curve diagrams to see the percentage error plotted on the graph for the angle and line for both adults and children. Doing this allows means to visually see where the relative averages are. Also as I am not plotting the actual results but the percentage error it is much easier to see the pattern of the estimation. Graph 1: This graph shows how the majority of the child's estimation of lines is similar to that of the angles, meaning that they are quite consistent in their estimations. But this is a crude method of finding this out. To obtain better, more accurate results I will need to use Spearmen's rank. Graph 2: This graph shows how the majority of the adult's estimation of lines is similar to that of the angles, meaning that they are quite consistent in their estimations. There are more consistent than the Childs estimations shown in graph 1.But again, this is a crude method of finding this out. To obtain better, more accurate results I will need to use Spearmen's rank. Graph 3: This shows the results of Spearmen's rank, the much more accurate method of finding the correlation in a graph. As you can see the overall result is -0.13. This shows that there is slight negative correlation Graph 4-7: These are the cumulative frequency curves for both adults and children's line and angle estimations. The lines drawn on indicate the IQR boundaries. On these we can the pattern of the estimations. On these it shows a massive increase of estimations within the IQR for the adults, much more than the children. This shows that more adults were estimating with the correct boundaries, showing their estimating we better, this evidence supports my hypothesis. Graph 8: This shows the method of obtaining the cumulative frequency curve, using the results. From this graphs I have gained more evidence but still not enough to gain a conclusion, therefore I will conduct an investigation of my own, with the school. Adam Baldwin ...read more.

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