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• Level: GCSE
• Subject: Maths
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# On average, I predict that's boys will be taller than girls.

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Introduction

Joe Nixon 11n                GCSE Maths Coursework

Mayfield High School

The idea of this project is to compare students’ data. The pupils that will be used are from Mayfield High School (renamed to protect data), ranging from years 7-11 and will be boys and girls. A lot of data has been collected from the school, ranging from age to the distance they travel to school. The project will attempt to reach conclusions regarding three specific stages. In answering these stages a range of sampling methods, presentation of data, and statistical calculations will be used in order to interpret and evaluate the data and come to a valid conclusion, drawing together all the data. Each stage will be presented and it will be explained what statistical methods will be involved in drawing conclusions for these questions.

Hypothesis 1: On average, I predict that’s boys will be taller than girls

This involves taking one piece of data from 30 boys and 30 girls randomly. I decided to choose the

Middle

1.75m

18

1.55m

19

1.76m

19

1.57m

20

1.78m

20

1.60m

21

1.79m

21

1.61m

22

1.79m

22

1.61m

23

1.80m

23

1.62m

24

1.80m

24

1.65m

25

1.81m

25

1.67m

26

1.81m

26

1.68m

27

1.81m

27

1.71m

28

1.82m

28

1.71m

29

1.82m

29

1.72m

30

1.90m

30

1.76m

Mode

1.81m

Mode

1.49m

Mean

1.70m

Mean

1.54m

Standard Deviation

0.113(3.d.p.)

Standard Deviation

0.123(3.d.p.)

Range

0.42m

Range

0.46m

Median from graph

1.75m

Median from graph

1.50m

Lower Quartile

1.67m

Lower Quartile

1.44m

Upper Quartile

1.80m

Upper Quartile

1.65m

Inter-quartile Range

0.13m

Inter-quartile Range

0.11m

Median

1.72m

Median

1.53m

Also see graphs

Observations:

As we can see from the table above:

• The average height of the boys’ was 1.70m and the girls’ was 1.54m.
• The shortest boy was 1.48m tall and the shortest girl was 1.30m tall, and the tallest boy was 1.90m tall and the tallest girl was 1.76m tall.
• My calculated median differs from the visual median from the cumulative frequency curve by 0.03m in the boys’ column and 0.03m in the girls’ column.
• 2/3 of the boys sample measured between 1.57m and 1.81m and 2/3 of the girls sample fell between 1.39m and 1.67m

Analysis and Conclusions:

I began this investigation with

Conclusion

This involves taking two pieces of data from 30 students selected at random. I decided to choose 30 students, as 30 for each set of data last time was enough to give me varied results helping me draw accurate conclusions about the data. I will then draw a scatter graph with a line of best fit and consider the results of the graph.

Initially we need to copy and paste the male data from its sheet back into its original place above the girls and then enter the following formula into excel to get a random number between 1 and 1184 (taking the column headings into account, adding an extra random number to compensate), to help me select pupils fairly:

=RAND()*1184

We then select the corresponding pupils and delete all of the data apart from the height and weight columns. NOTE- It does not matter whether the selection contains boys and girls. We then place this data into a table and draw the scatter graph, ensuring that the line of best fit is place on it. We can then comment on the graph and conclude.

 Height: Weight: 1 1.32 35 2 1.32 48 3 1.32 48 4 1.32 35 5 1.32 35 6 1.35 30 7 1.35 30 8 1.36 44 9 1.38 35 10 1.38 35 11 1.45 81 12 1.51 36 13 1.52 35 14 1.54 52 15 1.55 47 16 1.56 59 17 1.56 50 18 1.6 48 19 1.6 48 20 1.6 45 21 1.61 54 22 1.65 50 23 1.65 55 24 1.66 46 25 1.66 43 26 1.67 51 27 1.7 55 28 1.72 90 29 1.81 95 30 1.9 64

See Graph:

Observations:

From my graph, I cam see:

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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