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  • Level: GCSE
  • Subject: Maths
  • Word count: 3453

I have been given a set of data on a database from a fictitious school (Mayfield High School), but it is based on a real school. I have been given information about 1183 pupils; there is a variety of year 7, 8, 9, 10, and 11 both male and female.

Extracts from this document...

Introduction

Vicki Hawking 11 LD

Statistics Coursework

Introduction

I have been given a set of data on a database from a fictitious school (Mayfield High School), but it is based on a real school. I have been given information about 1183 pupils; there is a variety of year 7, 8, 9, 10, and 11 both male and female. This is the information I was given about each pupil: year group, age, month born, hair colour, eye colour, right or left handed, number of hours of T.V. watched per week, IQ, height, weight, distance to school, method of travel to school, key stage 2 results in English, maths, and Science. I will choose what I want to investigate and then get my data.

I have chosen for my investigation to use weight and height.

Hypothesis

I think that females have their main growth spurt before males, I am going to use the data to prove this.

Method

I will use 30 female pupils and 30 male pupils from a variety of years. I will get this information from the database. The data I will collect will be randomly picked from a large amount of data from a database. To insure it is a fair sample I will use stratified sampling, This will enable me to get my data so that it will all be in proportion. If I didn’t use stratified sampling then I could end up with ten year 11 and five year 7 when there are more year 7 in the school than year 11 and so my data would not be balanced.

...read more.

Middle

1.58

51

9

M

1.43

60

9

M

1.60

68

9

M

1.70

85

9

M

1.48

40

9

M

1.54

60

10

M

1.55

65

10

M

1.65

50

10

M

1.72

62

10

M

1.75

65

10

M

1.52

45

11

M

1.8

62

11

M

1.8

68

11

M

1.58

54

11

M

1.51

40

The Database

In the database there are some outliers, this will always happen. In my data I have a female in year 11 that weighs 30 kilograms. If I had a group of data where all my other females in year11 where 70 kilograms then the 30 kilogram girl would be an outlier. But because I have another female who weighs 38 kilograms it does not stand out so much. In my data I have some small people at 1.35 metres but I know you can get people at this size so it is not incorrect. I will use all my data even though some are outliers this is because I have a small number from each year and so if I didn’t use a piece of data then my results would be unbalanced.


Scattergram Analysis

My scattergrams suggest that the male distribution is a lot wider spread than the female distribution which are all around the same area. The scattergram implies that males grow at different ages rather than around the same age, it also implies that when males do grow they grow a lot more than females and that they put on more weight than females. There is no correlation on my female scattergram which suggest that height and weight aren’t related, whereas on my male data there is positive correlation which suggests that height and weight are related. The males scattergram suggests that they are about 1.50m in year 7 and grow 30 centimetres to 1.80 in year 11 this is a lot compared to the females who appear to start year 7 at 1.50 and grow approximately 20 centimetres to 1.70 in year 11. This shows that males and females start year 7 at the same size but in year 11 the males are a lot taller than females.

The female scattergram suggests that females weigh around 35 kilograms in year 7 and in year 11 weigh 65 kilograms whereas males weigh around 30 kilograms in year 7 and then weigh 70 in year 11 this again is a difference of 10 kilograms more than the females put on. The scattergrams suggest that males start year 7 smaller than the females but then end year 11 bigger than the females, this is why my females scattergram has a smaller range of height and weight.


A Stem and leaf Diagram of Weights

Females

Males

Year 7

2

3

5

Normal Distribution

555

4

35

Normal Distribution

70

5

0256

0

6

0

Year 8

Females

Males

2

6

Negatively skewed

3

8

Negatively skewed

775

4

8

3210

5

1336

Year 9

Females

Males

9770

4

0

4

5

1

Positively skewed

5

6

008

Normal Distribution

0

7

8

5

Year 10

Females

Males

8

4

5

Negatively skewed

8

5

0

Negatively skewed

000

6

255

Year 11

Females

Males

80

3

Positively skewed

5

4

0

Negatively skewed

6

5

4

6

28

...read more.

Conclusion

The average of female heights aren’t much help as the year 7 females average suggests that they are bigger than the year 8, 9 and 11. The year 10 females are about 1.63 metres according to the median and mean which sounds about right. The year 7, 8,  and 9 are all very close at 1.58/1.59 metres, this suggests that the females have their main growth spurt during year 9 as they are 5cm taller in year 10. My data says that the average year 11 female is 1.56cm tall this is because the year 11 females data I have are quite small. In year 8 and 11 the range is quite big which could account for the strange differences in height.

The average male in year 7 weighed 49.5 kilograms this is reasonable as they are quite small, their median is 51 kilograms which fits with the average. In year 8 there is a dramatic drop to an average at 46 kilograms, but their median suggest that this isn’t accurate as the median is again 51 kilogram. Year 9 males average is 60 kilograms, so is there mode and median. This implies that this is when males have there main growth spurt but in year 10 the average has dropped to 56 kilograms but the median is at 60. In year 11 the average is 56 with a median of 58 the range is 26 but this isn’t as big as year 9 where there is a difference of 45 kilograms. As there are very few pieces of data for year 10 and year 11 the average and median can easily be affected by an outlier so it is quite likely that the main growth spurt in boys were during year 8/9.

...read more.

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