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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.

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.

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.

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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# Related GCSE Height and Weight of Pupils and other Mayfield High School investigations essays

1. ## mayfield high statistics coursework

Here is the likelihood of a student being Left Handed from my sample: 0 1 I will now analyse data further in depth the sample that I have collected and form a Two Way Table that shows the boys and girls that are Right & Left Handed: Male Female Total

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

I have worked out the mean by multiplying each shoe size with its frequency. Once all these results were obtained I added them together, and divided by thirty. The range is the largest shoe size minus the smallest shoe size, which happens to be ten in each case.

1. ## Conduct an investigation comparing height and weight from pupils in Mayfield School.

w < 55 1 13 13 � 1 = 13 55 ? w < 65 2 5 5 � 2 = 2.5 (Please refer to the graph on page 17) From looking at the histogram for frequency density against weight you can see that there are; 10 people who weigh between 25 - 40kg.

2. ## The relationship between height and weight for students of Mayfield High School.

0,0,01,1,2,3,3,5,7,8,9,9 13 1.70 0,0,3,3,34,5,5,6 9 1.80 3, 1 1.90 2.00 Girls Weight Stem Leaf Frequency 30 8,8,8,9 4 40 4,5,5,6,8,8,8,8,8,8 10 50 0,0,0,1,2,4,4,4,46,6 11 60 0,0,0,4,5 5 70 80 90 Mean, Median, Mode and Range To help support the simple analysis from the previous section, comparing the mean, median, mode

1. ## Mayfield High School girl/boy height/weight investigation.

now create stem and leaf diagrams to show the Weights of both the males and Females in year 7... MALE WEIGHT Stem Leaf 2 5,6 3 7,8 4 0,0,1,3,4,5,5,5,8 5 0,3 Key: 2|5 = 25 m For the male stem and leaf diagram I have found: � Mode - 45

2. ## Statistics coursework - hypotheses based on students statistics

This judgement has been made purely by looking at the graphs and not by doing any sort of calculations yet. Below I have calculated Spearman's Correlation of Rank Coefficient: ~ Data point x y Rank x Rank y D D2 1 1.58 37 9 9 0 0 2 1.67 58

1. ## The aim of the statistics coursework is to compare and contrast 2 sets of ...

The first table will be for year 7. Height Tally Cumulative Frequency 131<h<140 ///// / 6 141<h<150 ///// 11 151<h<160 ///// ///// 21 161<h<170 ///// // 28 171<h<180 // 30 181<h<190 30 I will now do a frequency table for year 9.

2. ## Why the Book is Entitled Things Fall Apart

All of these factors served to drive the tribes of Umuofia apart and make them vulnerable, so that when the foreign influence of the white man was introduced, they were unable to help each other.

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