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• Level: GCSE
• Subject: Maths
• Word count: 5055

# I am going to investigate height. To begin with I will use a histogram to compare height throughout the school, then I will split this topic further to compare height of boys/girls. I will compare these with the national averages.

Extracts from this document...

Introduction

## PLAN

I am going to investigate height.  To begin with I will use a histogram to compare height throughout the school, then I will split this topic further to compare height of boys/girls.  I will compare these with the national averages.  Then I will investigate the hypothesis ‘the difference in height between boys in years seven and those in year 11 is greater than the difference in height between girls from the same years’.

## PROJECT

1. Throughout the school

I am going to use a histogram to compare the average height of students throughout the school.

## Why use a histogram?

Histograms (frequency density against height) are more appropriate than bar charts for displaying data with grouped frequencies for different ranges of values.   They have other advantages – it is clearer to display class intervals with low comparative frequencies if the class width is made wider for such intervals.  It will show the data clearly for comparison, displaying plainly which intervals of height have the greatest number of students and which have the fewest.

## Method

First I needed to take a stratified sample of students to represent the whole school.  As the sample is at random it ought to show the same results as a histogram of the whole school, just on a smaller scale.

Middle

7

1.70

7

1.56

7

1.42

7

1.51

7

1.63

7

1.56

7

1.63

7

1.60

8

1.43

8

1.70

8

1.72

8

1.55

8

1.65

8

1.44

8

1.75

8

1.41

8

1.73

8

1.51

8

1.70

8

1.65

8

1.54

8

1.59

8

1.45

8

1.73

8

1.75

8

1.72

8

1.73

8

1.60

8

1.44

9

1.58

9

1.52

9

1.69

9

1.54

9

1.60

9

1.60

9

1.60

9

1.56

9

1.55

9

1.40

9

1.52

9

1.65

9

1.61

9

1.50

9

1.65

9

1.76

9

1.53

9

1.51

9

1.70

9

1.60

9

1.53

9

1.71

9

1.51

9

1.70

9

1.58

10

1.65

10

1.72

10

1.75

10

1.75

10

1.56

10

1.65

10

1.80

10

1.70

10

1.50

10

1.55

10

1.41

10

1.73

10

1.67

10

1.62

10

1.60

10

1.72

11

1.50

11

1.63

11

1.55

11

1.72

11

1.65

11

1.61

11

1.63

11

1.57

11

1.56

11

1.61

11

1.63

11

1.63

11

1.57

11

1.55

11

1.80

The BOYS data I used in drawing a cumulative frequency graph and box plot.  It shows year and height.

 7 1.62 7 1.61 7 1.51 7 1.53 7 1.5 7 1.51 7 1.58 7 1.68 7 1.5 7 1.55 7 1.69 7 1.36 7 1.65 7 1.57 7 1.48 7 1.44 7 1.47 7 1.64 7 1.55 7 1.52 7 1.51 7 1.52 7 1.5 7 1.63 7 1.51 8 1.67 8 1.52 8 1.52 8 1.34 8 1.6 8 1.6 8 1.77 8 1.35 8 1.6 8 1.73 8 1.6 8 1.65 8 1.67 8 1.5 8 1.83 8 1.32 8 1.69 8 1.7 8 1.65 8 1.5 8 1.55 8 1.55 8 1.68 8 1.55 9 1.67 9 1.72 9 1.8 9 1.65 9 1.7 9 1.65 9 1.63 9 1.48 9 1.68 9 1.71 9 1.75 9 1.7 9 1.48 9 1.72 9 1.58 9 1.55 9 1.67 9 1.56 9 1.72 9 1.5 10 1.63 10 1.67 10 1.74 10 1.8 10 1.55 10 1.77 10 1.5 10 1.75 10 1.57 10 1.65 10 1.71 10 1.6 10 1.89 10 1.7 10 1.79 10 1.57 10 1.77 11 1.83 11 1.68 11 1.52 11 1.71 11 1.67 11 1.81 11 1.72 11 1.81 11 1.8 11 1.91 11 1.85 11 1.76 11 1.65 11 1.86

3. The height charts I used when making a global comparison using my data

The thickest red line in the middle is the average.  It shows that 50% are taller than the line and 50% are shorter.  The other four lines are also percentile lines.  For example, the one labelled 95 means that 95%

Conclusion

ass="c6">1.70

11

1.68

11

1.75

11

1.63

11

1.75

11

1.72

11

1.68

11

1.62

11

1.58

11

1.65

11

1.37

11

1.60

11

1.03

11

1.63

11

1.57

11

1.80

11

1.55

11

1.52

11

1.62

11

1.68

11

1.74

11

1.69

11

1.60

11

1.62

11

1.60

11

1.55

11

1.70

11

1.63

11

1.56

11

1.61

11

1.52

11

1.59

11

1.63

11

1.62

11

1.70

11

1.58

11

1.65

11

1.73

11

1.62

11

1.72

11

1.68

11

1.33

11

1.56

11

1.65

11

1.78

11

1.54

11

1.55

11

1.65

11

1.50

11

1.52

11

1.60

11

1.69

11

1.59

11

1.76

11

1.71

11

1.52

11

1.53

11

1.60

11

1.70

11

1.69

11

1.65

11

1.67

11

The BOYS data used when comparing the heights of year seven and year 11

 Height (m) Year 1.45 7 1.48 7 1.55 7 1.62 7 1.60 7 1.42 7 1.59 7 1.45 7 1.50 7 1.41 7 1.36 7 1.52 7 1.54 7 1.52 7 1.64 7 1.36 7 1.56 7 1.49 7 1.65 7 1.47 7 1.47 7 1.54 7 1.73 7 1.58 7 1.53 7 1.46 7 1.62 7 1.60 7 1.60 7 1.52 7 1.55 7 1.60 7 1.59 7 1.68 7 1.63 7 1.55 7 1.48 7 1.53 7 1.62 7 1.71 7 1.65 7 1.35 7 1.50 7 1.42 7 1.57 7 1.43 7 1.58 7 1.65 7 1.49 7 1.62 7 1.61 7 1.50 7 1.52 7 1.54 7 1.47 7 1.62 7 1.75 7 1.55 7 1.51 7 1.51 7 1.58 7 1.42 7 1.40 7 1.61 7 1.55 7 1.44 7 1.67 7 1.64 7 1.59 7 1.53 7 1.51 7 1.53 7 1.42 7 1.49 7 1.48 7 1.63 7 1.50 7 1.53 7 1.54 7 1.54 7 1.48 7 1.61 7 1.65 7 1.30 7 1.61 7 1.47 7 1.67 7 1.61 7 1.50 7 1.47 7 1.67 7 1.50 7 1.52 7 1.63 7 1.43 7 1.45 7 1.58 7 1.60 7 1.65 7 1.63 7 1.49 7 1.68 7 1.65 7 1.55 7 1.62 7 1.53 7 1.54 7 1.74 7 1.52 7 1.50 7 1.59 7 1.65 7 1.52 7 1.70 7 1.52 7 1.52 7 1.54 7 1.65 7 1.43 7 1.57 7 1.52 7 1.59 7 1.52 7 1.56 7 1.49 7 1.72 7 1.55 7 1.41 7 1.41 7 1.55 7 1.57 7 1.48 7 1.55 7 1.62 7 1.50 7 1.53 7 1.60 7 1.62 7 1.51 7 1.52 7 1.73 7 1.65 7 1.68 7 1.69 7 1.50 7 1.55 7 1.62 7 1.55 7 1.53 7 1.60 7 1.60 7 1.67 11 1.71 11 1.52 11 1.72 11 1.91 11 1.77 11 1.8 11 1.86 11 1.81 11 1.75 11 1.85 11 1.72 11 1.32 11 1.62 11 1.62 11 1.67 11 1.88 11 1.55 11 1.51 11 1.78 11 1.6 11 1.69 11 1.61 11 1.68 11 1.65 11 1.62 11 1.79 11 1.8 11 1.8 11 1.58 11 1.73 11 1.85 11 1.82 11 1.62 11 1.75 11 1.96 11 1.81 11 2 11 1.65 11 1.82 11 1.74 11 1.94 11 1.69 11 1.67 11 1.5 11 1.86 11 1.68 11 1.68 11 1.83 11 1.68 11 1.65 11 1.62 11 1.8 11 1.68 11 1.71 11 1.7 11 1.62 11 1.67 11 1.64 11 1.92 11 1.97 11 1.52 11 1.84 11 1.62 11 1.57 11 1.67 11 1.72 11 1.76 11 1.57 11 2.06 11 1.61 11 1.63 11 1.65 11 1.51 11 1.73 11 2 11 1.52 11 1.78 11 2.03 11 1.7 11 1.65 11 1.7 11 1.8 11 1.84 11

Stem and Leaf diagrams summarising this data

7G

11        9

12        055

13        001226

14        112222223355566777888888888899

15        0000001111222222223333344455666667788889999999

16        0000000111122222222233333344445556

17        023335559

18        00

11G

10        3

11

12

13        37

14

15        02222234555566678899

16        00000011122222223333333355555555778888889999

17        00001222233345568

18        03

7B

13        0566

14        0111222233345556777778888899999

15        00000000011112222222222223333333344444445555555555566777888899999

16        00000000111112222222223333445555555557778889

17        0123345

11B

13        2

14

15        0112225778

16        01122222223455555777778888899

17        000112223345567889

18        00000112234455668

19        12467

20        0036

A table displaying the values I used in drawing my stem and leaf diagrams

 BOYS GIRLS Year 7 (cm) Year 11 (cm) Difference (cm) Year 7 (cm) Year 11 (cm) Difference (cm) Minimum 130.00 132.00 2.00 119.00 103.00 -16.00 Lower Quartile 150.00 162.75 12.75 148.00 159.00 11.00 Median 155.00 170.00 15.00 154.00 163.00 9.00 Upper Quartile 161.50 180.25 18.75 162.00 169.00 7.00 Maximum 175.00 206.00 31.00 180.00 183.00 3.00

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