# Maths - Statistics

Extracts from this document...

Introduction

Contents Page

- Introduction
- Sample method
- Hypothesis
- Boy’s data
- Girl’s data
- Conclusion
- Stem and leaf diagrams
- Weight box plot
- Height box plot
- Box plots
- Scatter graph
- Comparing data
- CF graph – Height
- CF graph - Weight

1. Introduction

I am going to select at random 15 boys and 15 girls. There are 69 females and 55 males. The males and females are from a year seven class. Although there is a difference between how many boys and how many girls there are an equal sample from both is taken to simplify the test. We are picking an equal number of males and females for comparison between them and it will make it fair. This test will be useful to show me on how the year seven boys and girls differ in: Height, Weight, Hand span, Cubit and Foot size. I will then compare the data in several ways and it will end with me comparing data for the whole list of information.

## 2. Sample Data

I have chosen to use a sample data to make my chosen sample fair.

Middle

27

163

70

22

44

26

31

136

32

18

36

21

36

157

46

18

39

24

41

160

45

20

42

25

47

141

39

17

36

21

48

135

42

15

33

23

50

155

50

20

42

24

51

157

47

20

42

25

59

150

44

19

40

23

62

148

50

18

37

23

64

157

65

17

42

25

68

139

36

16

38

24

Total

149

46

18

39

23

- Conclusion

1.I conclude that my hypothesis was correct and boys are indeed taller than girls. I did this by calculating the means of the heights for both Boys + Girls.

2 .In my hypothesis in which I thought boys would be heavier than girls I was proven wrong; girls are in fact heavier than boys. I worked this out by calculating means as I did before.

3.In my prediction in which I said girls would have smaller feet than boys, my prediction was incorrect; girls have bigger feet than boys. I calculated this the same way as I did previously.

4. In the statement I wished to investigate in which I said girls would have smaller spans than boys. I was incorrect; girls have larger spans than boys. I calculated this the same way as before.

7. Stem and leaf diagrams

Height

I hypothesize that girls will have a more spread out data than the boys but the boys will have a higher median.

Girls | Boys | |

965 | 13 | |

98541 | 14 | 2445689 |

77750 | 15 | 12455679 |

30 | 16 |

Girls

Median | 149cm |

L. |

Conclusion

Height (See 9.)

My hypothesis about the spread of data for heights was correct. I was also correct that boys have a higher median than girls. I was also correct about girls having a higher I.Q.R than boys.

12. Comparing data

Hypothesis

I predict that the results from the whole data will be more precise and correct than the sample data. I think that none of the data will be the same.

Height

Males

Grouped | Frequency | Midpoint | Midpoint X Freq |

130 | 3 | 135 | 405 |

140 | 20 | 145 | 2900 |

150 | 29 | 155 | 4495 |

160 | 3 | 165 | 495 |

Total | 55 | 8265 |

Whole data - 8265/55 = 150.8cm

Sample data = 150.46cm

Females

Grouped | Frequency | Midpoint | Midpoint X Freq |

120 | 2 | 125 | 250 |

130 | 5 | 135 | 675 |

140 | 23 | 145 | 3335 |

150 | 28 | 155 | 4340 |

160 | 11 | 165 | 1815 |

Total | 69 | 10415 |

Whole data -10415/69 = 150.9cm

Sample data = 149cm

Weight

Males

Grouped | Frequency | Midpoint | Midpoint X Freq |

30 | 20 | 35 | 700 |

40 | 24 | 45 | 1080 |

50 | 6 | 55 | 330 |

60 | 2 | 65 | 130 |

70 | 2 | 75 | 150 |

80 | 1 | 85 | 85 |

Total | 55 | 2475 |

Whole data - 2475/55 = 45kg

Sample data = 42.8kg

Females

Grouped | Frequency | Midpoint | Midpoint X Freq |

20 | 3 | 25 | 75 |

30 | 11 | 35 | 385 |

40 | 29 | 45 | 1305 |

50 | 19 | 55 | 1045 |

60 | 5 | 65 | 325 |

70 | 2 | 75 | 150 |

Total | 69 | 3285 |

Whole data - 3285/69 = 47.6kg

Sample data = 46kg

Conclusion

My hypothesis was correct; the data was not the same. However the data was very close in some parts and this shows that using a sample method is nearly just as accurate as using the whole data.

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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