# I am investigating how well people estimate the length of a line and the size of an angle.

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Introduction

I am investigating how well people estimate the length of a line and the size of an angle. I am going to compare the following: * Year 7 compared to year 10 (Boys and girls) in estimating the size of an acute angle. * Girls compared to boys (Years 7 and 10) in estimating the length of a short line. I am going to compare these two because it is a very wide range of data. I am going to sample 40 people for each investigation, For example: * 40 people from year 7 and, * 40 people from year 10. A questionnaire has been circulated to a variety of people in set 1-5 and year 7-sixth form. The questionnaire includes questions, such as: * Estimate the length of this line * Estimate the size of this angle * Estimate the length of this squiggle For Investigation 1 'Year 7 compared to year 10 in estimating the size of an acute angle' My hypothesis is that a larger amount of year 10 will be better at estimating the size of an angle than year 7. I think that more people from year 10 will be better at estimating the size of an angle because they have been in education longer and are more advanced at maths, while year 7 will be less advanced as they haven't been in education as long as year 10. For Investigation 2 'Girls compared to boys I estimating the length of a short line' My hypothesis is that girls will be better at estimating the length of a line and the size of an angle than boys. I think that girls will be better at estimating the length of a line and the size of an angle than boys because girls take time to study things more closely than boys as boys tend to rush things. I will put all the data I collect in graphs. ...read more.

Middle

THAN YEAR 10. Hypothesis 2: Girls will be better at guessing the size of a short line than boys. Year 7 Females Stratified random sampling: 100 year 7 females in total. 20% of 100= 20. I will therefore take 20 samples. Estimates Error % error 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.45 0.05 3 1.6 0.1 7 1.6 0.1 7 1.6 0.1 7 1.7 0.2 13 1.2 0.3 20 1.2 0.3 20 1.9 0.4 26 1.9 0.4 26 2 0.5 33 1 0.5 33 0.2 1.3 86 Average Short line percentage error for Girls in year 7: 3 7 7 7 13 20 20 26 26 33 86 464 464- 20= 23.2% average Year 7 Males Stratified random sampling: 110 year 7 males in total. 20% of 110= 22. I will therefore take 22 samples. Estimate Error % error 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.6 0.1 7 1.25 0.25 17 1.2 0.3 20 1.2 0.3 20 1.9 0.4 26 1 0.5 33 2 0.5 33 2 0.5 33 2.25 0.75 50 2.5 1 67 2.5 1 67 2.5 1 67 0.04 1.46 97 3 1.5 100 3.2 1.7 113 3.4 1.9 127 3.4 1.9 127 3.4 1.9 127 Average Short line percentage error for Boys in year 7: 7 17 20 20 26 33 33 33 50 67 67 67 97 100 113 127 127 127 1131 1131- 22= 51.40909= 51.4% Year 10 Females Stratified random sampling: 80 year 10 females in total. 20% of 80= 16. I will therefore take 16 samples. Estimates Error % Error 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.5 0 0 1.6 0.1 7 1.6 0.1 7 1.3 0.2 13 1.3 0.2 13 1.7 0.2 13 1.7 0.2 13 1.8 0.3 20 1.8 0.3 20 1.9 0.4 26 1 0.5 33 2 0.5 33 Average Short line percentage ...read more.

Conclusion

1/2 37 37-2= 18.5 Median 1/4(36+1) 1/4 37 37-4= 9.25 Lower quartile boundary 3/4(36+1) 3/4 37 (37-4) x3= 27.45 Upper Quartile Boundary Cumulative frequency table leading onto box plot for hypothesis 2 (Girls will be better at guessing the size of a short line than boys) Year 7 and 10 males Groups Frequency Cumulative frequency 0- 12 12 10- 3 15 20- 5 20 30- 6 26 40- 0 26 50- 3 29 60- 7 36 70- 0 36 80- 0 36 90- 1 37 100- 1 38 110- 1 39 120- 3 42 Cumulative frequency: 42 1/2(42+1) 1/2 43 43-2= 21.5 Median 1/4(42+1) 1/4 43 43-4= 10.75 Lower quartile boundary 3/4(42+1) 3/4 42 (43-4) x3= 32.25 Upper Quartile Boundary COUNCLUSION Hypothesis 1: MY HYPOTHESIS WAS PROVED INCORRECT AS ON AVERAGE THE PERCENTAGE ERROR FOR THE ESTIMATION OF AN ACUTE ANGLE WAS LOWER FOR YEAR 7 THAN FOR YEAR 10, MEANING YEAR 7 WERE MORE ACCURATE AND CLOSER TO THE CORRECT NUMBER (ON AVERAGE) THAN YEAR 10. Hypothesis 2: MY HYPOTHESIS WAS PROVED CORRECT AS ON AVERAGE THE PERCENTAGE ERROR FOR THE ESTIMATION OF A SHORT LINE WAS LOWER FOR FEMALES THAN FOR MALES, MEANING FEMALES WERE MORE ACCURATE AND CLOSER TO THE CORRECT NUMBER (ON AVERAGE) THAN MALES. I have evidence in the form of graphs and average calculations to prove my conclusion. My hypothesis works on a base of average. I ruled out all anomalous results before stratifying my samples to avoid biased results which may lead me to conclude my hypothesizes wrong. I think hypothesis 1 was incorrect because among Year 10 we had a few results which were a large percentage error (127%) this bought up my average and made my hypothesis worng. I could improve my project and got better results my sampling more data so I got a more accurate average and by taking out all even slightly anomalous results to stop them from bringing the average percentage error up. To develop my task further, I could have gone on to look at another part of the questionnaire i.e. the estimation of a short squiggle. ...read more.

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