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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.

image00.png

image06.png

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

image10.png

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

...read more.

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

image11.png

image12.png

To better compare this data I drew a frequency polygon

image01.png

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.

...read more.

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.

...read more.

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