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• Level: GCSE
• Subject: Maths
• Word count: 3026

# In this coursework I am going to investigate about height and weight of students from Mayfield. Mayfield is a fictious high school but the data that I am going to use is based on a real school that wants to stay anonymous.

Extracts from this document...

Introduction

BOYS

## GIRLS

TOTAL

7

151

131

282

8

145

125

270

9

118

143

261

10

106

94

200

11

84

86

170

MATHS COURSEWORK

In this coursework I am going to investigate about height and weight of students from Mayfield. Mayfield is a fictious high school but the data that I am going to use is based on a real school that wants to stay anonymous.

The following data was provided:

The total number of students in Mayfield High School is 1183.

There will be data provided on each student such as:

• Name
• Year Group
• Gender
• Candidate number
• Weight
• Height

I am going to investigate the following:

1. Height
2. Weight

To extend my coursework I will find out the difference between the weight and height of girls and boys.

Line of inquiry

The aim is to find out the height and weight of the students and the relationship between them.

My theory is the taller the person the heavier they are likely to be.

## Collecting data

In this investigation I will take a random sample of 30 students from the school statistics. Plus we will be recording their gender, height and weight. I will then look at the average height and weight of the sample chosen.

There is a lot of way to get a random sample of students for example write the candidate number from 1 to 1183 and then put it I to a hat and then pick them out, but this can take a lot of time.

Middle

II

2

180 < h < 190

I

1

Pie chart

The Pie chart below represents the weight of the students.

The Pie chart below represents the height of the students.

Looking at the bar and pie chart from the previous page I have noted the following statements….

(1*38) + (1*39) + (1*40) + (1*41) + (1*43) + (1*44) + (2*45) + (1*47) + (2*48) + (2*49) + (1*50) + (2*51) + (1*52) + (1*53) + (1*54) + (1*56) + (2*57) + (1*59) + (³*60) + (1*62) + (1*64) + (1*66)

=

1 + 1 + 1 + 1 + 1 + 1 + 2 + 1 + 2 + 2 + 1 + 2 + 1 + 1 + 1 + 1 + 2 + 1 + 4 + 1 + 1 + 1

The mean weight of the students = 51.6 kg

(1*135) + (1*148) + (1*150) + (2*152) + (1*154) + (2*156) + (1*157) + (2*159)

+ (3*160) + (3*162) + (2*163) + (1*164) + (2*165) + (2*166) + (3*167) + (1*170) + (1*175) + (1*180)

=

1 + 1 + 1 + 2 + 1 + 2 + 1 +2 + 3 + 3 + 2 + 1 + 2 + 2  + 3  + 1 + 1 + 1

The mean height of the students = 160.7 cm

The modal weight of the students = 40 < w < 50cm = 11 students

The modal height of the students = 160 < h < 170cm = 16 students

The median weight of the student = 51 kg.

The median height of the student = 162 cm.

The range for the weight = 28 kg.

The range for the height = 45 cm.

Overall

These results show that there are only a few people from the sample who are tall than 170 cm and there is only one person who is shorter than 140 cm. More than 50% of the students in the sample are 160 < h < 170 cm tall. There are only two students who weigh between 30 < w < 40. 11 out of 30 students from the sample weigh between     < 40 w < 50 and another ten students weigh between 50 < w < 60.

## Extending the investigation

I am now going to look at the sample in more depth. I will extend my investigation upon the line of enquiry and give my self and hypothesis to test. This statement can either be true or false.

I will test the hypothesis by looking at a different data. I will extend my investigation by looking at the height and weight between boys and girls. I am going to start by testing the following hypothesis.

In general the taller the person height the heavier he is likely to be in weight.

## New Sample

Inorder to investigate the difference between boys and girls I will be to taking a new sample using my previous method. I will take a sample of 15 boys and 15 girls in order to make it equivalent.

## Second sample

 Student ID Gender Height Weight 1 F 1.53 40 2 F 1.48 37 3 F 1.64 47 4 F 1.73 51 5 F 1.42 52 6 F 1.75 57 7 M 1.36 45 8 M 1.47 50 9 M 1.54 53 10 M 1.65 35 11 M 1.59 47 12 F 1.48 46 13 F 1.57 46 14 F 1.65 49 15 M 1.52 60 16 M 1.61 48 17 M 1.50 52 18 F 1.50 65 19 M 1.52 52 20 M 1.71 68 21 F 1.60 56 22 F 1.80 60 23 F 1.75 50 24 F 1.52 70 25 M 1.63 60 26 M 1.65 64 27 M 1.77 72 28 F 1.72 60 29 M 1.71 57 30 M 1.61 42

Tally chart shown below represents the heights of the students.

## Table 1

Height, h (cm)

Tally

Frequency

130 < h < 140

#### I

1

140 < h < 150

IIII

³

150 < h < 160

IIII IIII

9

160 < h < 170

IIII III

8

170 < h < 180

IIII II

7

180 < h < 190

I

1

Tally chart shown below represents the weights of the students.

Weight, w (kg)

Tally

30 < w < 40

2

40 < w < 50

IIII IIII

9

50 < w < 60

IIII IIII

10

60 < w < 70

IIII II

7

70 < w < 80

II

2

## Table 3: Boys height

Height, h (cm)

Tally

Frequency

130 < h < 140

#### I

1

140 < h < 150

I

1

150 < h < 160

IIII

5

160 < h < 170

IIII

5

170 < h < 180

III

3

180 < h < 190

0

Conclusion

• The points on the scatter diagram for boys & girls are less dispersed than the points on the scatter graph for Mixed. This suggests that the correlation between height and weight is better when boys and girls are considered separately.
• Cumulative frequency curves confirm that boys are heavier than girls in weight.
• The median height for girl is higher than the medium height for boys.

One of the main limitations that I had within the investigation was that the average mean on height always was higher for girls than boys.

I might’ve been able to have a better result if I chose to research upon a larger quantity of students.

Doing this whole investigation I have found out that not all of the hypothesis can be true. Some of them can have its own downside, which means you can’t predict a perfect outline to the relationship. Though most of the results backs up my hypothesis by saying the taller you are the heavier you would likely to be.

Cumulative Frequency Graphs

Cumulative frequency can be a very powerful tool when comparing different data sets. This table shows the cumulative frequency for Height on boys, girls and mixed.

## Cumulative Frequency

Height (m)

Boys

Girls

Mixed

<140

1

0

1

<150

2

3

5

<160

7

7

14

<170

12

10

22

<180

15

14

29

<190

15

15

30

Heights (m)

### Median

Lower Quartile

Upper Quartile

Inter-quartile Range

Mixed

161.5

152.5

170.5

170.5-152.5=18

Boys

160

153.5

164

164-153.5=10.5

Girls

160

151.5

173.5

173.5-153.5=22

## Cumulative Frequency

Weight (kg)

Boys

Girls

Mixed

<40

1

1

2

<50

6

5

11

<60

11

10

21

<70

14

14

28

<80

15

15

30

Weights (kg)

### Median

Lower Quartile

Upper Quartile

Inter-quartile Range

Mixed

54

46

61.5

15.5

Boys

53.4

45

61.5

14.5

Girls

54.5

45.5

64.5

64.5-45.5=19

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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