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  • Level: GCSE
  • Subject: Maths
  • Word count: 3348

height and weight investigation

Extracts from this document...

Introduction

Introduction

In this assignment my aim is to investigate differences between height and weight in different year groups of boys and girls in Mayfield High School. However this is a very general aim therefore I will also try to find out whether it is true that girls in year 11 weigh less than girls in year 9, or when boys start growing faster than girls. This will also make my investigation a lot more interesting. In order to make it simpler for me I will use stratified random sampling of 10% of the total number of students in Mayfield High School.

Stratified Sampling

This is the method used to gather information randomly; this is also the method I will use in this assignment. I chose to use a sample of 10% if the students in Mayfield High School.

The table below shows the total number of boys and girls in each year group.

Year Group

Pupils

Boys

Girls

Year 7

282

151

131

Year 8

270

145

125

Year 9

261

118

143

Year 10

200

106

94

Year 11

170

84

86

I want to get 10% of the total number of students; however stratified sampling refers to getting percentage in proportion, therefore I will multiply each number in this table by 0.1. The results are shown in the table below.

Year Group

Pupils

Boys

Girls

Year 7

28

15

13

Year 8

28

15

13

Year 9

26

12

14

Year 10

20

11

9

Year 11

17

8

9

Now I have 10% of every year group and gender and I know how many boys and girls I need from each year group to form my data. To get the information about the heights and weights from the database I need to generate the numbers of boys and girls from Mayfield High School (in the database each is student is represented by a number from 1 to 1183).

...read more.

Middle

8

1.50 up to but not including 1.60

36

1.60 up to but not including 1.70

39

1.70 up to but not including 1.80

23

1.80 up to but not including 1.90

6

1.90 up to but not including 2.00

1

2.00 up to but not including 2.10

1

Weight, w (kg)

Frequency

30 up to but not including 35

3

35 up to but not including 40

10

40 up to but not including 45

15

45 up to but not including 50

30

50 up to but not including 55

25

55 up to but not including 60

21

60 up to but not including 65

6

65 up to but not including 70

3

70 up to but not including 75

4

75 up to but not including 80

0

80 up to but not including 85

1

85 up to but not including 90

1

Using the information shown in these tables I will plot 2 histograms, one for each. I will do this also using Excel.image00.png


image01.png

These graphs show me the frequency of the heights and weights of the whole sample. From them I can see that most of the students are 1.60 m to 1.69 m tall and weigh 45 kg to 49 kg.


Male and Female

I now have a lot of information about the whole sample of Mayfield High School. Now I will break it down to male and female categories and compare the information to show different facts, like girls are taller than boys in year 7 but boys are taller then girls in year 9. First I will find out the same information I found out for the whole sample, the mean, mode, median, range and standard deviation for both heights and weights.

Boys

These are the statistics for the heights of all the boys in Mayfield High School:

Mean: 1.62 m

Median: 1.62 m

Mode: 1.70 m

Range: 0.80 m

Standard deviation: 0.14 m

These statistics show the following facts:

  • The most common high in Mayfield High School is 1.70 meters tall (as the mode is 1.70). This is very unusual as the mean height is 1.62 meters (there is a difference of 8 cm between the mode and the mean).
  • According to the range there is a big height difference between the tallest boy and the shortest one, 80 cm.
  • The standard deviation in this case proves that the mean reflects most of the data is the average deviation from the mean is not too big which means that most of the data is quite near the mean.
...read more.

Conclusion

-19.72, so the equation is y=43.16×1.65+(-19.72).

y = 43.16×1.65+(-19.72)

y = 71.21+(-19.72)

y = 51.50

Therefore I predict that a 1.65 meters tall female will weigh 51.50 kg.

Comparing individual year groups

In the early parts of this investigation I proved that as a person gets taller he/she also gains weight (no matter if it’s a boy or a girl). Now I would like to see if girls are heavier in year 9 than in year 11. The easiest way to compare the two year groups is to draw a cumulative frequency diagram, however this time I will draw the graph by hand because cumulative frequency almost the only graph that Excel can’t draw accurately. Firstly I will draw 2 cumulative frequency tables, one for each year group, to help me plot the graph.

Year 9

Year 11

weight

frequency

Cumulative

 frequency

weight

frequency

cumulative frequency

30≤kg<35

0

0

30≤kg<35

0

0

35≤kg<40

2

2

35≤kg<40

2

2

40≤kg<45

1

3

40≤kg<45

1

3

45≤kg<50

7

10

45≤kg<50

7

10

50≤kg<55

2

12

50≤kg<55

2

12

55≤kg<60

1

13

55≤kg<60

1

13

60≤kg<65

0

13

60≤kg<65

0

13

65≤kg<70

0

13

65≤kg<70

0

13

70≤kg<75

1

14

70≤kg<75

1

14

75≤kg<80

0

14

75≤kg<80

0

14

80≤kg<85

0

14

80≤kg<85

0

14

85≤kg<90

0

14

85≤kg<90

0

14

After the cumulative frequency I will plot box and whiskers diagrams.

Year 9

Year 11

Minimum

35

35

Maximum

60

70

Median

43

44.5

Lower quartile

40.5

41.5

Upper quartile

45.5

54



The cumulative frequency diagram on the previous page shows me that girls in year 11 are heavier than girls in year 9, which mean that my hypothesis is wrong. This is because the year 11 curve is on the right side of the year 9 curve which means that the x values are bigger. I can also see these interesting statistics:

Year 9:

Median – 43 kg

Upper quartile – 45.5 kg

Lower quartile – 40.5 kg

Inter quartile range – 5 kg

Year 11:

Median – 44.5 kg

Upper quartile – 54 kg

Lower quartile – 41.5 kg

Inter quartile range – 12.5 kg

The box and whiskers diagram shows me more clearly that year 11’s median is slightly bigger and that there is much bigger spread of weights in year 11.

...read more.

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