Statsics Of 50 Pupils

Statistics Coursework

My hypothesis is that the taller you are the more you weigh. I believe this because the taller you are the more body mass you have you have. So you will therefore weigh more than someone who is short, as they will have a smaller body mass making them lighter.

For sampling I will get my data from a database about all the children who are between the ages of 14, 15, and 16 in years 10 and 11 in Deneshaw School. I will need this information about the pupil from the database:

• Weight

• Height

• Gender

• Year group

In trial runs on a small sample of random data, I found that I needed to use stratified data to get the right amount of year 10’s and 11’s (26 year 10’s, and 24 year 11’s). I also found that gender might affect my results; as females are generally seem to be smaller, than males.

I chose to have 50 people/pupils as my sample size, as I think this is an appropriate amount because it is not too much data to deal with, and it gives enough variety.

Here are tables for the 50 pupils, which show their weight, height, gender and year group. I have made a table for each year group and gender i.e. year 10 boys.

This is the data I will be using to create graphs, histograms, and cumulative frequency curves.

I will now put this data from the tables into scatter graphs to show what the data looks like and how it differs from my hypothesis. I will make 4 different graphs 2 for year 10’s that will be split into males and females. I will do the same for year 11. The reason for this is that the year 11’s may be taller than the younger year 10’s as they have had longer to grow and develop. I have split the sexes up because males will have more body mass than girls and this would affect the results I could get.

From these scatter graphs you can see that the majority of pupils follow my hypothesis. The only exception is �Table A’ were it only just different. Table A has the least correlation and if anything it is negative. I found that the year 11’s follow my rule better than the year 10’s, and females follow it better than males.

Mean

I will now find an estimate for the mean heights and weights for each year separately i.e. year 10 heights’. I have chosen to put the males and females together, because if they were separate it would be impractical as there would be too many tables etc.

Firstly I added the frequencies of the males and females and got a total. Then I found the mid-points of the heights and then I multiplied that by the total frequency’s to get the fx. Now I can find the mean, the formula for this is пÑ"Ґfx/пÑ"Ґf

I will now apply this to the my tableвЂ¦Ð²Ð‚¦Ð²Ð‚¦

44.05 / 26= 1.7 m to 1dp

The mean height for Year 10’s is 1.7m to 1dp

I will now do the same for the other heights and weights.

WorkingвЂ¦Ð²Ð‚¦Ð²Ð‚¦

1475.4 / 26= 56.7 kg to 1dp

The mean weight for Year 10’s is 56.7 kg to 1dp

Year 11 Frequency (f)

Height (m) Males Females Total Mid-Point (x) fx

1.30<1.35 1 0 1 1.325 1.325

1.35<1.40 0 0 0 1.375 0

1.40<1.45 0 0 0 1.425 0

1.45<1.50 0 0 0 1.475 0

1.50<1.55 2 0 2 1.525 3.05

1.55<1.60 1 2 3 1.575 4.725

1.60<1.65 1 5 6 1.625 9.75

1.65<1.70 2 0 2 1.675 3.35

1.70<1.75 3 2 5 1.725 8.625

1.75<1.80 0 0 0 1.775 0

1.80<1.85 2 2 4 1.825 7.3

1.85<1.90 1 0 1 1.875 1.875

Total= 24 40

WorkingвЂ¦Ð²Ð‚¦Ð²Ð‚¦

40 / 24= 1.7 m to 1dp

The mean height for Year 11’s is 1.7 m to 1dp

Year 11 Frequency (f)

Weight (kg) Males Females Total Mid-Point (x) fx

30<35 0 0 0 37.5 0

35<40 1 0 1 42.5 42.5

40<45 1 3 4 47.5 190

45<50 2 2 4 52.7 210.8

50<55 1 5 6 57.2 343.2

55<60 1 0 1 62.5 62.5

60<65 4 0 4 67.5 270

65<70 1 0 1 72.5 72.5

70<75 1 0 1 77.5 77.5

75<80 0 0 0 82.5 0

80<85 1 1 2 87.2 174.4

Total= 24 1443.4

WorkingвЂ¦Ð²Ð‚¦Ð²Ð‚¦