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• Level: GCSE
• Subject: Maths
• Word count: 1735

Investigation of shoe size and height from Mayfield high school database.

Extracts from this document...

Introduction

Maths Coursework

Holly Budgen 10G

Investigation of Shoe Size and Height from Mayfield High School Database

INTRODUCTION

I will use the fictional database from Mayfield High School to do my investigation. I would like to investigate the relationship between:

• Boy’s height and girl’s height
• Boy’s shoe size and girl’s shoe size
• Boy’s height to shoe size ratio
• Girl’s height to shoe size ratio
• The differences between the two ratios

This will show me the gender variation. I will use a sample of 30 boys and 30 girls from the original 1183 students in the database. I will take a fair sample by using random sampling. I will take a stratified sample of 120, and from this I will use a random number table to get the desired 60 students, which I will base my investigation on.

From these 60 samples I will work out the mean, median, mode and range to research the topic. I will create graphs and pie charts to analyse the information I will collect. I feel this will assure the observations I make are successful. I will be able to compare them successfully and make a valid conclusion.

SAMPLE

Below is the data I have collected:

 7 1.63 5 1.61 11 1.57 11 1.55 9 1.72 7 1.65 11 1.67 10 1.74 12 1.88 9 1.7 4 1.8 7 1.73 12 1.67 3 1.33 13 2.06 2 1.65

Middle

1.40-1.49

2

1.50-1.59

9

1.60-1.69

11

1.70-1.79

5

1.80-1.89

1

30

 Boys Height Height Tally Frequency 1.50-1.59 10 1.60-1.69 9 1.70-1.79 6 1.80-1.89 4 1.90-1.99 0 2.00-2.09 1 30

I have worked out the mean, median, mode and range for the height in similar ways as for the shoe size. I worked out the mean by multiplying the frequency by the mid point of each group. I added up all of these results and then divided by thirty. The median, mode and range are the same as for the shoe sizes.

The figures I have worked out from the data seem quiet promising, and already I have observed:

• The differences between the boy’s shoe size mean and the girl’s shoe size mean,
• The differences between the boy’s height mean and the girl’s height mean,
• The difference between the range in girl’s height and boy’s height,
• And many more observations can be made.

From this data I will make a stem and leaf diagram.

STEM AND LEAF DIAGRAMS

 Boys Height Stem Leaf Frequency Cumulative frequency 1.50 2,4,4,5,5,7,7,8,9,9 10 10 1.60 0,2,3,3,5,6,7,7,7 9 19 1.70 2,2,2,3,3,5 6 25 1.80 0,0,2,8 4 29 1.90 0 29 2.00 6, 1 30 Girls Height Stem Leaf Frequency Cumulative frequency 1.30 2,3 2 2 1.40 3,5 2 4 1.50 1,1,2,2,3,4,5,5,7 9 13 1.60 0,0,1,1,2,3,5,5,5,5,5 11 24 1.70 0,0,3,3,4 5 29 1.80 0, 1 30

A stem and leaf wouldn’t be appropriate for shoe size so I only mad them for height. They are very useful, as they will help me make a cumulative frequency graph

CUMULATIVE FREQUENCY

VARIENCE

Conclusion

The cumulative frequency graph I have drawn is useful too. It shows the differences between boy’s height and girl’s height, of which there are lots. They both follow the same pattern, but boys on average are clearly taller than girls.

CONCLUSION

After my successful collected sample, I feel I presented the data well, allowing myself to make some good observations. Now I feel I am able to conclude my results.

• I have clearly proven that on average, boy’s feet are larger than girl’s feet.
• I have also proven boys on average are taller than girls
• From the graphs the slight positive correlation shows that with girls and boys, when height increases so does shoe size.

If I wished, I could research this subject further, perhaps by using a larger sample of boys and girls, or perhaps by using more accurate measurement, (perhaps heights to one decimal place). If I had measured the boys and girls myself, it may have been a more accurate investigation. But overall, considering the data I had to complete the investigation, I feel it turned out well. I am happy with the results I have collected and feel I have made a valid conclusion.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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