# The average male and female in Year 10 students in England

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Introduction

Sagar Malik

Statistics Coursework

Introduction

For my statistics coursework I will be looking at the average male and female in Year 10 students in England to try and find out what they are like. In finding this out I will be looking at the physical characteristics of male and female Year 10 students such as Height, IQ, Number of siblings and Number of pets. When I have collected my data I will examine it and use various statistical methods such as arithmetic means. I will also draw pictorial representations of my data such as cumulative frequency graphs and box plots to find out the interquartile range and the median.

I needed 60 samples altogether, which consisted of male and female Year 10’s, because it would have been easier to recover the results then doing Year 10 and Year 11. However, the results consisted of 30 male students and 30 female students.

The random number I used was in a random number list, the direction which I chose my random numbers went right across my page in the direction of right. I used the numbers to find the name of the children in a database and then gather personal details to put in a new database.

Middle

96

1.91

116

1.55

101

1.75

102

1.61

94

1.91

113

1.26

95

1.55

107

1.42

91

1.42

88

1.51

101

1.66

91

1.72

104

1.42

101

1.66

105

1.26

94

1.76

116

1.31

89

1.65

91

1.65

131

1.63

101

1.42

112

1.34

111

1.87

124

1.72

94

1.77

109

1.63

96

1.79

113

1.73

104

1.84

116

1.63

91

1.84

116

1.63

95

1.21

111

1.32

121

1.62

116

1.81

92

1.91

112

1.57

103

1.75

103

1.65

115

1.75

111

1.55

94

1.81

117

1.65

129

1.33

84

1.67

101

1.66

99

1.68

114

1.89

117

1.61

87

1.71

106

1.91

94

1.77

112

1.26

91

1.23

91

1.75

102

Frequency Polygon

This is a good way of comparing continuous data by drawing a frequency polygon.

Boys

Height, h (cm) | Tally | Frequency | C.F |

120<h<130 | 3 | 3 | |

130<h<140 | 2 | 5 | |

140<h<150 | 3 | 8 | |

150<h<160 | 1 | 9 | |

160<h<170 | 5 | 14 | |

170<h<180 | 8 | 22 | |

180<h<190 | 5 | 27 | |

190<h<200 | 3 | 30 |

Girls

Height, h (cm) | Tally | Frequency | C.F |

120<h<130 | 3 | 3 | |

130<h<140 | 2 | 5 | |

140<h<150 | 1 | 6 | |

150<h<160 | 4 | 10 | |

160<h<170 | 12 | 22 | |

170<h<180 | 5 | 27 | |

180<h<190 | 2 | 29 | |

190<h<200 | 1 | 30 |

The reason there is an extra column showing the Cumulative Frequency, is due to the following Cumulative Frequency Curve graphs on the following pages.

Since the data is grouped into class intervals, it also makes sense to record it in a stem and leaf diagram. This will make it easier to read off the median values.

Boys

Stem | Leaf | Frequency |

120 | 1,3,6 | 3 |

130 | 1,3 | 2 |

140 | 2,2,2 | 3 |

150 | 5 | 1 |

160 | 2,5,6,6,6 | 5 |

170 | 1,5,5,5,7,7,7,9 | 8 |

180 | 1,4,4,7,9 | 5 |

190 | 1,1,1 | 3 |

Girls

Stem | Leaf | Frequency |

120 | 1,6,6 | 3 |

130 | 2,4 | 2 |

140 | 2 | 2 |

150 | 1,5,5,7 | 4 |

160 | 1,1,3,3,3,3,5,5,5,6,7,8 | 12 |

170 | 2,2,3,5,6 | 5 |

180 | 1,1 | 2 |

190 | 1 | 1 |

Averages

It is also possible to record the mean, median and range for the data. Due to the data being continuous it makes more sense to find the modal class interval rather than the mode. This is the class interval that contains that most values. The values for the mode and median have been rounded to two decimal places.

Heights (cm) | Mean | Modal Class Interval | Median | Range |

Boys | 165 | 170-180 | 173 | 70 |

Girls | 160 |

Conclusion

From the frequency table above the mean number of siblings is:

Σfx(1x0)+(18x1)+(8x2)+(1x3)+(1x4)+(1x5)46

Σf 1+18+8+1+1+1 30

Mean Number of Pets = 1.53

In conclusion, although there are a small number of boys with a small number of siblings and boys with a small number of pets, the evidence suggests that, in general, the number of siblings for the boys is greater the number of pets for boys.

Spearman’s Rank Correlation Coefficient

This will be used to find the extent to which two sets of data correlate.

Number | No. of siblings | Rank | No. of Pets | Rank | d | d² |

9 | 1 | 1 | 1 | 2 | 1 | 1 |

1 | 2 | 2 | 1 | 2 | 0 | 0 |

4 | 2 | 2 | 1 | 2 | 0 | 1 |

6 | 2 | 2 | 1 | 2 | 0 | 0 |

7 | 2 | 2 | 1 | 2 | 0 | 0 |

11 | 2 | 2 | 0 | 1 | -1 | -1 |

17 | 2 | 2 | 2 | 20 | 18 | 324 |

18 | 2 | 2 | 2 | 20 | 18 | 324 |

19 | 2 | 2 | 1 | 2 | 0 | 0 |

20 | 2 | 2 | 1 | 2 | 0 | 0 |

26 | 2 | 2 | 1 | 2 | 0 | 0 |

28 | 2 | 2 | 1 | 2 | 0 | 0 |

30 | 2 | 2 | 1 | 2 | 0 | 0 |

2 | 3 | 14 | 1 | 2 | -12 | -144 |

5 | 3 | 14 | 1 | 2 | -12 | -144 |

8 | 3 | 14 | 1 | 2 | -12 | -144 |

12 | 3 | 14 | 2 | 20 | 6 | 36 |

14 | 3 | 14 | 1 | 2 | -12 | -144 |

16 | 3 | 14 | 2 | 20 | 6 | 36 |

22 | 3 | 14 | 2 | 20 | 6 | 36 |

24 | 3 | 14 | 1 | 2 | -12 | -144 |

25 | 3 | 14 | 1 | 2 | -12 | -144 |

27 | 3 | 14 | 1 | 2 | -12 | -144 |

3 | 4 | 24 | 2 | 20 | -4 | -16 |

15 | 4 | 24 | 2 | 20 | -4 | -16 |

23 | 5 | 26 | 3 | 28 | 2 | 4 |

10 | 6 | 27 | 5 | 30 | 3 | 9 |

13 | 6 | 27 | 1 | 2 | -25 | -625 |

21 | 7 | 29 | 4 | 29 | 0 | 0 |

29 | 7 | 29 | 2 | 20 | -9 | -81 |

-976 |

Σd² = 116

There are 30 samples, so n = 30

rs = 1 - 6Σd²

n(n²-1)

= 1 - 6x-976

30(900-1)

= 1 - -976

26970

= 1 – 0.0258 = 0.9

0.9 is a high agreement between the number of pets and number of siblings.

Cumulative Frequency Curves

For the Frequency Tables, please look at the heading; Tally Chart

The benefit of drawing cumulative frequency curves for a continuous variable like number of siblings and number of pets is that it is easy to read off the graph to retrieve the median, upper quartile, lower quartile and interquartile range:

Number of Siblings

Median | Lower Quartile | Upper Quartile | Interquartile Range |

2.1 | 1.8 | 2.9 | 1.1 |

Number of Pets

Median | Lower Quartile | Upper Quartile | Interquartile Range |

0.9 | 0.7 | 1.1 | 0.4 |

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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