Adam Warlow. Pg 2
I put this data into a set of pie charts as pie charts can often make data easier to recognise and understand. I will do pie charts of height and weight for both years 10 and 11. I will also do a frequency table to be able to see the modal class for each year.
Adam Warlow. Pg 3
Frequency Tables - Height.
Year 10 Year 11
Here are two tables representing the height of students in year 10 and in year 11.
By looking at the two tables, I can see that the modal class for each year group is 1.60 – 1.75 metres. The difference is huge in year 10 but in year 11 the difference is very small and by looking at the data it could be said that more people in year 10 are taller which is very surprising.
Percentages for Pie Charts.
Year 10 Year 11
Adam Warlow. Pg 4
Pie Charts – Height.
Year 10
Year 11
Adam Warlow. Pg 6
Frequency Tables – Weight.
Year 10 Year 11
Here are the two tables representing the weight of students in years 10 and 11. The modal class for year 10 is 50 < w <60 but the modal class for year 11 is 60 < w <70. This data was expected as it is generally older people who weigh more.
Percentages for Pie Charts.
Year 10 Year 11
Adam Warlow. Pg 7
Pie Charts – Weight.
Year 10
Year 11
Adam Warlow. Pg 8
Pie Charts.
The first set of charts and tables show that each year group has a spread of data between 1.0 metre and 2.05 metres, and using these class boundaries, the modal class is the same for both years. Also in both years most people are 1.60 metres tall or taller. For weight, each year group has a spread between 30kg’s and 90kg’s but each year has a different modal class with year 10’s being 50 < w <60 and year 11’s being 60 < w <70.
I will now calculate the mean, median, quartiles, range and standard deviation for each year group:
Height.
Year 10
Mean = ∑x = 53.49 = 1.67
n 32
There are 32 pieces of data so the median is halfway between the 16th and 17th, the lower quartile is halfway between the 8th and 9th, and the upper quartile is halfway between the 24th and 25th.
Minimum value: 1.41
8th value: 1.60, 9th value: 1.60 so Lower Quartile = 1.60
16th value: 1.68, 17th value: 1.70 so Median = 1.69
24th value: 1.74, 25th value: 1.75 so Upper Quartile = 1.745
Therefore, the inter quartile range = 1.745 – 1.60 = 0.145
Maximum Value: 1.90
Therefore, Range = 1.90 – 1.41 = 0.49
Adam Warlow. Pg 10
Year 11
Mean = ∑x = 46.08 = 1.65
n 28
There are 28 pieces of data so the median is halfway between the 14th and 15th; the lower quartile is halfway between the 7th and 8th, and the upper quartile halfway between the 21st and 22nd.
Minimum Value: 1.03
7th value: 1.55, 5th value: 1.56 so Lower Quartile = 1.555
14th value: 1.67, 15th value: 1.67 so Median = 1.67
21st Value: 1.76, 22nd value: 1.77 so Upper Quartile = 1.765
Therefore the inter quartile range = 1.765 – 1.555 = 0.21
Maximum Value: 1.83
Therefore, range = 1.83 – 1.03 = 0.8
By comparing the two sets of data I can see that:
- The year 11 data has a larger range, almost double.
- The mean averages show that year 10 students are generally taller than year 11 students.
- The year 11 data has a larger inter quartile range and therefore is more spread out.
On the next page I will now look at the distribution of weight figures in years 10 and 11:
Adam Warlow. Pg 11
Year 10 Weight
Mean = ∑x = 1814 = 56.69
n 32
Minimum value: 50
8th Value: 48, 9th value: 50 so Lower quartile = 49
16th value: 55, 17th value: 56 so Median = 55.5
24th value: 60, 25th value: 64 so Upper quartile = 62
Therefore, Inter quartile range = 62-49 = 13
Maximum value = 80
Therefore Range = 80-50=30
Year 11 Weight
Mean = ∑x = 1503 = 53.68
n 28
Minimum value = 38
7th value: 45, 8th value: 45 so Lower quartile = 45
14th value: 54, 15th value: 54 so Median = 54
21st value: 60, 22nd value: 62 so Upper quartile = 61
Therefore, inter quartile range = 61-45=16
Maximum value = 72
Therefore, range = 72-38=34
Adam Warlow. Pg 12
By comparing these two sets of data I can see that:
- Year 11 have a slightly higher range and inter quartile range.
- The mean and median values are quite similar for both sets of data.
- The mean weight of year 10’s is higher than the mean weight of year 11’s.
Conclusions so far:
- Year 10’s both have higher mean weight and higher mean height than the year 11’s. This is very surprising as I thought this figure would be the other way round as I thought that the older you are the taller you are and the more you weigh.
- Although year 10 have a higher average weight, year 11 have a greater spread of weight across the year.
- The above statement is also true for height with year 11’s height being spread out more across the year group.
- The hypothesis that states “children that weigh more are generally taller” seems to be true as pupils in year 10 are both taller and weigh more on average. However, I feel more evidence is needed to fully prove my hypothesis.
So now I will prove my hypothesis to be correct by using scatter graphs:
-
Year 10:
Here there is a strong positive correlation suggesting that a pupil who is taller also weighs more.
Adam Warlow. Pg 13
- Year 11:
This graph is very similar to that of year 10 as it clearly shows a strong correlation suggesting that a pupil who is taller also weighs more.
Conclusion
My hypothesis that taller people will weigh more has been proved correct through this investigation. There is a strong correlation, which suggests that the two sets of data are related as I thought. However, my theory that the older you are the taller you are and therefore the more you weigh have been shown to be incorrect has year 10 pupils had both a higher average height and weight. This may be because the figures given by the pupils were incorrect.
Evaluation
In order to make this investigation more accurate and reliable I could have used a much bigger sample. Although this would involve a lot more time being spent and more calculations, the accuracy of the investigation would be much better and this may show and even stronger correlation and even prove my theory that the older you are, the taller you are and therefore the more you weigh.
However, I have only looked at a sample of the data, the sample was taken randomly and I have not been bias at any time throughout the investigation so I do believe that my conclusion is correct and that there is a strong correlation between height and weight of pupils in year 10 and in year 11.