• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15
16. 16
16
17. 17
17
18. 18
18
19. 19
19
20. 20
20
21. 21
21
22. 22
22
23. 23
23
24. 24
24
• 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).

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.

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.

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.

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.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Height and Weight of Pupils and other Mayfield High School investigations essays

1. ## A hypothesis is the outline of the idea/ideas which I will be testing and ...

(25-18)] + [3 X (35-18)] 30 V 1/30 = 0.0333 4.dp Conclusion From the Standard Deviation that I have come to find how spread out the data that I have used in my sample for this particular hypothesis and measure of the dispersion of the data and has helped me

2. ## An Investigation into the height to length ratio of Limpets on exposed and sheltered ...

However, on the sheltered shores, the wave action is less violent. This allows the limpet to attend to other issues with which it has to cope with. Here, it can afford to have a large height and uses this to its advantage by storing water in the extra space.

1. ## In this coursework I want to find out what the average height, weight, and ...

spread of the middle 50% of data for Males is slightly more than the spread of the data for Females. I can see that the median for females is a much lower length than the median for males. I can also clearly see that there are no females with a

2. ## I will be testing the following hypothesis in my pilot study: ...

will help to support my hypothesis as box and whisker diagrams can show the overall shape of the distribution, median, quartiles and help you compare two different sets of data if you have drawn two of them. This involves the height and weight because if the mean, standard deviation and

1. ## My investigation is to explore the average student.

159 163 170 160 175 Weight (kg's) 66 62 77 70 63 Left/Right R L R R R Shoe size 6 7 9 8 10 Hand span 19 20 22 18 23 Hair Colour Ginger Brown Blonde Brown Blonde Eye Colour Brown Hazel Brown Green Green Money per month (�)

2. ## mayfield course work -boys are generally heavier than girl. This has to do with ...

1.67 6.68 1.7 - 1.74 0 1.72 0 1 1.72 1.72 1.75 - 1.79 2 1.77 3.54 5 1.77 8.85 1.8 - 1.84 3 1.82 5.46 1.85 - 1.89 1 1.87 1.87 ?f = 10 ?fx = 16.55 ?f = 10 ?fx = 17.452 Estimated mean = 16.55 = 17.452

1. ## Hypothesis&amp;quot;The taller you are, the bigger is your foot length&amp;quot;. I think my hypothesis ...

24 30625 576 4200 144 24 20736 576 3456 171 23 29241 529 3933 166 27 27556 729 4482 154 23 23716 529 3542 151 25 22801 625 3775 163 23 26569 529 3749 151 21 22801 441 3171 141 23 19881 529 3243 167 24 27889 576 4008 150

2. ## Mayfield igh Investigation

The year 7 boys and girls box plots show that the interquartile ranges are very similar to each other, and are very close. However, the range of the box plot is huge with the girls, but much smaller with the boys.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to