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  • Level: GCSE
  • Subject: Maths
  • Word count: 2241

'Who is the Average Pupil in Year 11?'

Extracts from this document...

Introduction

Rebecca Austin 11Y

Maths Coursework

‘Who is the Average Pupil in Year 11?’

Introduction

This investigation will be to find out what students in year 11 general appearance are and what they can do. I will find the ‘average’ student by using the data we have received.

To do this investigation I will need data such as height, weight, waist, and whether a pupil can swim or not. I will be using secondary data because I feel it will be more reliable.

I will use a sample size of 50. I will use a sample size of 50 because I feel it is a good even number, which is small enough to handle, but yet big enough to show the spread of data. To decide which 50 pupils I will use, and their sexes, I will take the number of boys in the year and then divide by the overall number of pupils in year 11 and then multiply by the sample size. I will do the same for the girls.

Number of boys/girls in year 11

Number of pupils in year 11                X sample size

...read more.

Middle

8

1

1

3

1

3

1

8

1

3

1

1

Mode = Size 6

Mean = 3 + 3.5 + (4 x 3) + 4.5 + (5 x 3) + 5.5 + (6 x 8) + 6.5 + (7 x 3) + 7.5 + 8        

                                                         24

        = 5.6

        = Size 5.5

Median = 3 3.5 4 4 4 4.5 5 5 5 5.5 6 6 6 6 6 6 6 6 6.5 7 7 7 7.5 8

         = Size 6

For shoe sizes I would think mode is the best way to display the data because it shows which size shoe is actually the most popular.

Pie Charts

Shoe Sizes

Boys

Shoe

Sizes

Angle on pie chart

(1.d.p)

5  

6

6.5

7

7.5

8

8.5

9

10

1

1

3

3

1

9

2

2

4

1/26 x 360 = 13.8

1/26 x 360 = 13.8

3/26 x 360 = 41.5

3/26 x 360 = 41.5

1/26 x 360 = 13.8

9/26 x 360 = 124.5

2/26 x 360 = 27.7

2/26 x 360 = 27.7

4/26 x 360 = 55.4

14

14

41.5

41.5

14

124.5

28

28

55.5

*See pie chart on next page

Histograms

Weights

To show weight for boys and girls in year 11 I will draw histograms, which will show the data in both the height of the bar but also in the area.

Boys

Weight

Frequency

Frequency Density

40< w < 45

45< w < 55

55< w < 65

65< w < 75

75< w < 85

2

8

12

3

1

2/5 = 0.4

8/10 = 0.8

12/10 = 1.2

3/10 = 0.3

1/10 = 0.1

0.4

0.8

1.2

0.3

0.1

*See graph on next page

Girls

Weight

Frequency

Frequency Density

35< w < 45

45< w < 55

...read more.

Conclusion

-     11.4

10.6

-     16.4

 5.6

 9.6

 3.6

 3.6

 0.6

 4.6

108.16

29.16

21.16

29.16

213.16

0.16

29.16

158.76

5.76

0.36

0.36

5.76

134.56

1.96

40.96

179.56

1.96

129.96

112.36

268.96

31.36

92.16

12.96

12.96

0.36

21.16

 .x = 170.4

= 1642.36

Standard diviation = √∑(x  x)   = 1642.36

                                        .n                     26

                               = 7.9 (1.d.p)

Percentages and Bar Graphs

Can/Cannot Swim, Left/Right Handed and Can/Cannot Roll Tongue

I will use percentages to display the amount of pupils in year 11 who can or cannot do the things above. These results will be shown in a bar graph and will be done for both boys and girls.

Boys – swimming

Can swim

24

24/26 x 100 = 92.3

92%

Cannot swim

2

2/26 x 100 = 7.7

8%

Girls – swimming

Can swim

22

22/24 x 100 = 91.7

92%

Cannot swim

2

2/24 x 100 = 8.3

8%

Boys – left/right handed

Right handed

2

2/26 x 100 = 7.7

8%

Left handed

24

24/26 x 100 = 92.3

92%

Girls – left/right handed

Left handed

4

4/24 x 100 = 16.7

17%

Right handed

20

20/24 x 100 = 83.3

83%

Boys – Rolling tongue

Can roll

18

18/26 x 100 = 69.2

69%

Cannot roll

8

8/26 x 100 = 30.8

31%

Girls – Rolling tongue

Can Roll

14

14/24 x 100 = 58.3

58%

Cannot Roll

10

10/24 x 100 = 41.6

42%

Conclusion

After carrying out this investigation, I found the following points:

  1. Males are taller generally than females and most of the time have a bigger shoe size
  2. Boys mainly do weigh more than girls then the data is not more evenly spread out as I predicted.
  3. More people can swim compared to the amount that cannot
  4. More pupils in year 11 are right handed, and more boys are right handed (92%) to the amount of girls (83%)
  5. The percentage of pupils who can roll their tongue is greater then those who cannot, but it seem to be more dominant in boys

...read more.

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