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

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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

### 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

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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