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• Level: GCSE
• Subject: Maths
• Word count: 3530

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

Extracts from this document...

Introduction

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

I am going to use secondary data for my investigation. The data is based on a real school but the name of the students and the school has been changed. The data is presented as a single list of 1183 pupils, from year 7 to year 11. I have chosen to investigate one line of inquiry. The relationship between height and weight. I will choose a sample of thirty boys and thirty girls randomly. This can be done using a number of methods. I have used a website to do this.

### Height and Weight

Below I have shown the sample of the thirty boys and girls that I have chosen.

 Girls Girls Boys Boys Height (m) Weight (kg) Height (m) Weight (kg) 136 44 132 38 142 52 149 67 152 33 150 55 152 55 153 40 154 45 154 42 156 50 154 54 156 53 155 38 156 63 155 43 156 74 155 47 157 45 155 47 157 52 155 64 157 53 155 64 158 40 160 55 158 48 162 48 158 55 162 49 160 42 162 50 160 54 165 46 161 54 165 50 162 42 165 54 162 65 166 43 163 45 166 54 163 48 168 63 165 52 173 50 170 48 174 64 170 50 177 57 172 45 178 67 172 50 180 68 175 53 180 77 175 72 182 75 178 59 183 75

Next I represented this data in the form of a frequency table with boys and girls separately

### GIRLS

 Height, h (cm) Frequency Tally 130 ≤ h < 140 1 140 ≤ h < 150 1 150 ≤ h < 160 13 160 ≤ h < 170 8 170 ≤ h < 180 7 180 ≤ h < 190 0

### BOYS

 Height, h (cm) Frequency Tally 130 ≤ h < 140 1 140 ≤ h < 150 1 150 ≤ h < 160 10 160 ≤ h < 170 10 170 ≤ h < 180 4 180 ≤ h < 190 4

I next started drawing diagrams show to represent my data. I started analyzing the data using histograms. I used histograms because the data was continuous.

A better comparison of this data can be made using a frequency polygon.

Since the data is grouped into class intervals, I have recorded it in a stem and leaf diagram so to make it easier to find the median.

### GIRLS

 Stem Leaf Frequency 130 6, 1 140 2, 1 150 2, 2, 4, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8 13 160 0, 0, 1, 2, 2, 3, 3, 5 8 170 0, 0, 2, 2, 5, 5, 8 7 180 0

### BOYS

 Stem Leaf Frequency 130 2, 1 140 9, 1 150 0, 3, 4, 4, 5, 5, 5, 5, 5, 5 10 160 0, 2, 2, 2, 5, 5, 5, 6, 6, 8 10 170 3, 4, 7, 8 4 180 0, 0, 2, 3 4

I also recorded the mean, modal class interval, median and the range so to better compare the data.

 Height (cm) Mean Modal class interval Median Range Girls 160.43 150-160 159 42 Boys 163 150-160-170 162 51

Middle

Here is the weight of boys and girls represented in a table.

### GIRLS

 Weight, w (kg) Frequency Tally 30 ≤ w < 40 1 40 ≤ w < 50 11 50 ≤ w < 60 14 60 ≤ w < 70 2 70 ≤ w < 80 2

### BOYS

 Weight, w (kg) Frequency Tally 30 ≤ w < 40 2 40 ≤ w < 50 9 50 ≤ w < 60 9 60 ≤ w < 70 7 70 ≤ w < 80 3

Then I drew the histograms

To better compare this data I drew a frequency polygon

Since the data is grouped into class intervals, I have recorded it in a stem and leaf diagram so to make it easier to find the median.

### GIRLS

 Stem Leaf Frequency 30 3, 1 40 0, 2, 2, 4, 5, 5, 5, 5, 8, 8, 8 11 50 0, 0, 0, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 9 14 60 3, 5 2 70 2, 4 2

### BOYS

 Stem Leaf Frequency 30 8, 8 2 40 0, 2, 3, 3, 6, 7, 7, 8, 9 9 50 0, 0, 0, 4, 4, 4, 5, 5, 7 9 60 3, 4, 4, 4, 7, 7, 8 7 70 5, 5, 7 3

I also recorded the mean, modal class interval, median and the range so to better compare the data.

 Weight (kg) Mean Modal class interval Median Range Girls 51.37 50-60 51 41 Boys 54.8 40-50-60 54 39

As seen in the table above boys have a greater mean and median yet the modal class interval is higher for the girls. The mean for the boys is higher because there are a greater number of boys with a height greater the 60 than girls, 6 boys more. So the mean is higher. The median is also higher for the boys for the same reasons. So I can conclude by saying that more boys have a greater weight then girls. Also from looking at the data I can say that the weight of the girls is more concentrated between 40kg to 60kg while the weight of the boys is more widely spread out. About 14 out of 30 girls or 46.66% of the girls have a weight between 50kg to 60kg while 9 out of 30 boys or 30% of the boys have a weight between 50kg to 60kg. The same numbers of boys have a weight between 40kg to 50kg.

Conclusion

. It tells us how spread out the data is from the mean.

The method to calculate the standard deviation is as follows:

For each value x, which is the midpoint of the class interval, subtract the overall average x| from x, then multiply that result by itself (otherwise known as determining the square of that value) and then divide it by the frequency f. Sum up all these values. Then divide that result by sum of all the frequencies. Then, find the square root of that last number. Below I have shown the formula for this.

∑ [f(x-x|) 2]

∑f

Now I will calculate the standard deviation of the boys’ height.

 x x-x| (x-x|)2 f f(x-x|)2 135 135-163 = -28 784 1 784 145 145-163 = -18 324 1 324 155 155-163 = -8 64 10 640 165 165-163 = 2 4 10 40 175 175-163 = 12 144 4 576 185 185-163 = 22 484 4 1936 Totals ∑f = 30 ∑f(x-x|)2 = 4300

Standard deviation = √ (4300/30)

Standard deviation for boys’ height = 11.97

Now I will calculate the standard deviation of the girls’ height.

 x x-x| (x-x|)2 f f(x-x|)2 135 135-160.43 = -25.43 646.68 1 646.68 145 145-160.43 = -15.43 238.08 1 238.08 155 155-160.43 = -5.43 29.48 13 383.24 165 165-160.43 = -4.57 20.88 8 167.04 175 175-160.43 = 14.57 212.28 7 1485.96 185 185-160.43=24.57 603.68 0 0 Totals ∑f = 30 ∑f(x-x|)2 = 2921

Standard deviation = √ (2921/30)

Standard deviation for girls’ height = 9.87

The standard deviation for boys is greater then that of the girls by 2.10. So I can say that the values for the boys are more spread out then that of the girls.

Now I will calculate the standard deviation of the boys’ weight.

 x x-x| (x-x|)2 f f(x-x|)2 35 35-54.8 = -19.8 392.04 2 784.08 45 45-54.8 = -9.8 96.04 9 864.36 55 55-54.8 = 0.2 0.04 9 0.36 65 65-54.8 = 10.2 104.04 7 728.28 75 75-54.8 = 20.2 408.04 3 1224.12 Totals ∑f = 30 ∑f(x-x|)2 = 3601.20

Standard deviation = √ (3601.20/30)

Standard deviation for boys’ height = 10.96

Now I will calculate the standard deviation of the girls’ weight.

 x x-x| (x-x|)2 f f(x-x|)2 35 35-51.37 = -16.37 267.98 1 267.98 45 45-51.37 = -6.37 40.58 11 446.35 55 55-51.37 = 3.63 13.18 14 184.48 65 65-51.37 = 13.63 185.78 2 371.55 75 75-51.37 = 23.63 558.38 2 1116.75 Totals ∑f = 30 ∑f(x-x|)2 = 2387.11

Standard deviation = √ (2387.11/30)

Standard deviation for girls’ height = 8.92

The standard deviation for boys is greater then that of the girls by 2.04. So I can say that the values for the boys are more spread out then that of the girls.

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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