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  • Level: GCSE
  • Subject: Maths
  • Word count: 2421

Mayfield High School is a school for students aged 11-16. Although fictional, the data is based on a real school.

Extracts from this document...

Introduction

Benjy Masher 11LF

Maths Coursework

Mayfield High School is a school for students aged 11-16. Although fictional, the data is based on a real school.

This table shows how many boys and girls there are in Mayfield:

Year Group        

Number of Boys

Number of girls

Total

7

150

150

300

8

145

125

270

9

120

140

260

10

100

100

200

11

84

86

170

The total number of students is 1200

Data is provided on each student as

Name, Age, Year group, IQ, Weight, Height, hair colour, eye colour, shoe size, Distance from home to school, Usual method of travel to school, number of brother or sisters, Key stage 2 results in English, Mathematics and Science, Key Stage 3 results in English, Mathematics and Science.

There are a number of possible lines of inquiry one can take including

  • The variations in hair colour,
  • The variations in eye colour,
  • The relationship between the above two colours,
  • Shoe sizes,
  • The distances travelled to school,
  • The relationship between shoe size and height,
  • The relationship between two sets of key stage 2 and/or 3 results,
  • The relationship between IQ and Key stage results,
  • The height to weight ratio in terms of the body mass index.

In my project I will be investigating the relationship between height and weight

Collecting the data

I will begin taking a random sample of 30 boys and 30 girls from the database of the schools pupils, and recording their height and weight.

...read more.

Middle

45

1.60

60

1.72

45

1.70

60

1.55

60

1.63

45

1.55

50

1.55

50

1.55

50

1.69

50

1.65

52

1.62

54

1.58

45

1.62

46

1.65

54

1.70

48

1.73

64

1.73

48

1.57

48

1.33

55

1.63

48

1.75

60

1.58

36

1.63

38

1.72

56

1.75

56

1.61

59

1.63

48

1.58

48

1.67

48

1.68

48

1.65

59

Averages

Heights (cm)

Mean

Modal class interval

Median

Range

Boys

172

160-170

170

40

Girls

162

160-170

163

42

Weights (kg)

Mean

Modal class interval

Median

Range

Boys

59

50-60

57

37

Girls

51

40-50

48

28

Since all the data is continuous it makes more sense to use the modal class interval (the class interval that contains the most values) rather then the mode.

Height:

Out of three measures of averages the boys mean and median were higher then that of the girls. The modal class interval was equal. But, the range of the boys was 0.4m compared to the girls who had 0.42m this meant that the girls heights were more spread out. The evidence from the sample suggest that 11 out of 27 boys, or 41% have a height between 160-170cm, whilst 15 out of 33, or 45% of the girls have a height between 160-170cm. The frequency polygons show that there are fewer boys with heights below 140cm than girls.

Weight:

Out of the three measures of averages all three of them were higher for boys than girls, with a range of 0.37kg compared to 0.28kg for the girls. The evidence for the sample suggests that 13 out of 27, or 48% of the boys have weights between 50-60kg, whilst 14 out of 33, or 42% have weights between 40-50kg. The frequency polygons show that there are more girls under 50kg then there are boys.

...read more.

Conclusion

Considering Age

Since age would definitely affect height or weight it would seem necessary for us to mention that

When age is taken into consideration, the correlation between weight and height will be better that when age is not considered.

Summary of results and conclusion

There is a positive correlation between height and weight. In general the heavier you are the taller you are likely to be.

As only 27 boys were collected and 33 girls it is hard to give a precise analysis on the scattering of the points on the diagram. But, as it is there are more points closely around the line of best fit in the scatter diagram for boys then there are for girls. This suggests that boys heights correlation is better then that of the girls height and this also means that the boys heights is less predictable.

The points on the scatter graph are more dispersed  then the points on the mixed population graph, this suggest that there is a better correlation when they (boys and girls) are considered together.

Since the mixed population graph does not need a curve line of best fit the overall relationship is not linear.

Estimates can be made, by either reading off the graph or using the equation of the line of best fit

The median height of the boys is larger than the girls

We would’ve had better results if there were more data collected, as this is what would make the results more accurate and reliable.

...read more.

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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