In this coursework I want to find out what the average height, weight, and arm span of a Year 11 pupil is

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Philip Davies 11B                                          8th February 2005

The Average Year 11 Pupil

Hypothesis

   In this coursework I want to find out what the average height, weight, and arm span of a Year 11 pupil is. I think that my height, and arm span will be 10% more than the average Year 11 pupil, and my weight will be 5% more than the average year 11 Pupil, I want to find out if this is correct. I will also compare the height, weight, and arm span of an average Year 11 male to an average Year 11 female, because I think that an average Year 11 male will be 10% taller, heavier, and have a 10% longer arm span than an average Year 11 female. Finally, I want to find out if an average Year 11 pupil is square, and if an average Year 11 male is squarer than an average Year 11 female. The calculations and graphs that I am going to make are;

   Each pupil in Year 11 measured their own height, weight, and arm span, and all the data was collected and put in a table. So the data we are using is Primary Data because we have collected it. The sampling which I used to get my data was systematic sampling. To get better results I left out any sets of data with missing measurements. I chose every 4th set of data and recorded it in a table. I decided to choose 25 male, and 25 female sets of data, so I will have 50 sets of data. Here is the data that I have selected;

   Here are my measurements;

   There are no sets of data in the table which stand out, so I believe the data is all genuine. The data that I have collected is Continuous data so I will have to group my data for the 3 measurements.

1. Height (All data)

   I will now do all my calculations and graphs for Height. I will firstly do the calculations and graphs for all of my data, and then I will split the data into male and female and complete the calculations and graphs for them. Here is my table of grouped data for height, including all my data;

1. Histogram

   From the Histogram above I can see that there are more pupils with a smaller height than pupils with a larger height. I can also see that there is a slight negative skew in the Histogram which shows that there is a bigger distribution of smaller pupils in Year 11.

2. Mean

     Mean =         Sum of Height  =        8491.6  =  169.832cm

                 No. of Pupils           50

   Compared to my height of 182cm, the mean height for Year 11 pupils is 169.832cm, which would make me above average height by 12.1cm. As a percentage this would mean I am 6.6% taller than the mean height of a Year 11 pupil, so my hypothesis was almost correct.

3. Mode (Modal Group)

     Mode (Modal Group) = 165 ≤ h < 170 cm

   The modal group height for a Year 11 pupil is 165 ≤ h < 170 which is

17cm < h ≤ 12cm smaller than my height which means I am 9.3% ≤ h < 6.6% taller than the average Year 11 pupil.

4. Cumulative Frequency Graph

   Here is the table and graph for Cumulative Frequency;

   From the Cumulative Frequency graph above I can see that the gradient of the curve is steeper below the median height, and that the gradient is not as steep for the taller people above the median. This shows that the heights of the smaller pupils seem to be closer together, and the heights of the taller people seem to be more spread out.

5. Median

     Median = 169cm

   The median height of a Year 11 pupil is 169cm, this is 13cm (7.1%) smaller than my height. This shows my prediction of 10% is almost correct.

6. Interquartile Range

     Interquartile Range   =   Q3 – Q1   =   178cm – 163cm   =   15cm

   

   From this diagram and the Interquartile Range I can see that the middle 50% of the data covers almost exactly half of the total data range, so it has got a normal spread. I can also see that the lower 50% of the data is closer together, and the higher 50% of the data is more spread out.

7. Standard Deviation

     Standard Deviation = 9.52

   The Standard Deviation measures how the data are dispersed from the mean. So from this figure I can see that the data values are spread widely from the mean because the standard deviation is high, this means that there is a large dispersion.

   

   From the calculations I have made for Height I have found out that I am between 6.6% and 9.3% taller than the average Year 11 Pupil. In my hypothesis I predicted I was 10% taller, so I was not far off.

1. Height (Male & Female)

   I will now split the data into male and female because I want to find out if an average Year 11 Male has a 10% bigger height than an average Year 11 Female. I will repeat the calculations and graphs, and compare the two sets of answers I get as I go along. Here are the two tables of grouped data for Male and Female Heights;

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  1. Histogram

   These Histograms show that Year 11 males are taller than Year 11 females. The Histogram for Year 11 Males has a Positive Skew, and the Histogram for Year 11 females has a negative skew, which shows that on average there are mainly tall males, and on average the females are small. I can also see that there are very few tall females, and few small males.

2. Mean

   Mean Male Height  =         Sum of Height  =        4401.4  =  176.056cm

                                       No. of Pupils            25

   Mean Female Height ...

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