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Introduction

Mayfield High School Data:

Hypothesis:

My hypothesis is year 11 boys taller and weighs more then year 11 girls.

Introduction:

From the data I have received I have chosen to perform an investigation comparing height and weight because I feel there’s much relevance between ones and height and weight.  I have chosen to compare height and weight because I feel I will get clear results and therefore perform a meaningful investigation.  I will be trying to determine whether ones height has any bearing to ones weight by separating boys from girls from year 11. This will show accurate results to prove my hypothesis.

Sampling:

To get a completely unbiased sample of students I will be using random selection. I am going to get my data by picking every third person this will be a completely random and unbiased way of choosing my students. From this I will want to get 25 boys and 25 girls. I have chosen this sampling method because I think it is the most appropriate. It will also enable me to test my hypothesis fairly.

I used an auto filter to sort the data out by year groups and put them in boys and girls. I decided to pick my data by picking every third person on the list. This would have enabled me to pick out people by random. Also my sample won’t be biased

Middle

10

17

2,3,7,9

4

18

1,2,4

3

19

2,4,6

3

Total

25

150+152+155+157+158+162+  162+163+165+165+167+168+  168+168+169+172+173+177+ 179+181+182+184+192+194+ 196

25

= 170 CM

Boys Weight Stem & Leaf:

 Stem Leaf Frequency. 3 5 1 4 5,7 2 5 0,0,0,4,4,4,5,6,7,8,8,8,9 13 6 0,0,3,6 4 7 2,2,8 3 8 0 1 9 3 1 Total 25

35+45+47+50+50+50+54+54+ 54+55+56+57+58+58+58+59+ 60+ 60+63+66+72+72+78+80+ 93

25

= 59 KG

Girls Height Stem & Leaf:

 Stem Leaf Frequency. 13 3 1 14 0 15 2,2,7,8,8 5 16 0,0,0,1,2,2,3,3,3,3,5,5,8,8 14 17 0,2,4,5,8 0 Total 25

133+152+152+157+158+158+ 160+160+160+161+162+162+ 163+163+163+163+165+165+ 168+168+170+172+174+175+  178

25

= 162 CM

Girls Weight Stem & Leaf:

 Stem Leaf Freq. 3 8,8,9 3 4 2,4,4,5,7,8,8,8,8,8 10 5 4,4,4,4,5,5,6,9 9 6 0,3,6,6 4 Total 25

38+38+39+42+44+44+45+47+48+48+ 48+48+48+54+54+54+54+55+55+56+ 59+ 60+63+66+66

25

= 51 KG

Summary Of Stem & Leaf:

 Height(cm) Mean Median Range Boys 170 168 46 Weight(kg) Mean Median Range Boys 59 58 58 Height(cm) Mean Median Range Girls 162 163 45 Weight(kg) Mean Median Range Girls 51 48 28

Conclusion For Height  Boys And Girls:

The mean height of the boys is higher than the mean height for the girls.

The median for the boys is higher than the girls, also the range of the girls 0.46m and is extremely close to the boy’s range of 0.45m.The Stem & Leaf diagram shows that more girls than boys have a height less than 160cm, but more boys than girls have a height more than 170cm. These results are based on a random sample of 25 boys and 25 girls from year 11.

Conclusion For Weight Boys And Girls:

The mean height of the boys is higher than the mean height for the girls. The median for the boys is higher than the girls by 10, which means the girl’s weight have a lot more smaller value than the boy’s weights.  The range for the boys is 0.58 and is extremely higher than the girl’s range which is 0.28; this is because for boys the highest weight for the boys is 93kg which is 27kg higher than the girl’s highest weight which is 66kg. The Stem & Leaf diagram shows that more girls than boys have a weight less than 60kg, but more boys than girls have a weight more than 60kg.  These results are based on a random sample of 25 boys and 25 girls from year 11

Scatter Graphs to look for correlation and relation between boy and girls in year 11. Also attempt to prove my hypothesis The graph above shows that there is a positive correlation with most of the results shows that the taller you are the more you weigh. The graph above shows no correlation. In this graph it shows that  height does not affect your weight when it comes to girls.

Standard Deviation:

I now will make comparisons between the year 11 students.  I think this will give me good information on how much change there is between boys and girls in year 11.  I will be doing standard deviation to find out whether how much the deviation of height and weight from the mean will differ from boys to girls. From doing this investigation I will have established that better and clearer results are obtained when boys and girls are separated.  So for the standard deviation I will be comparing year 11 boys to the year 11 girls.

I predict that the boys in year 11 will have greater Standard Deviations for both height and weight.  The reason for this prediction is that by year 11 boys will be taller and generally weigh more then the year 11 girls. Plus the range on heights and weights will be more, and so therefore the deviation about the mean will be less strong.  So therefore the deviation of the range of heights and weights will be more accurate.

Standard deviation so I will be able to see whether boys or girls have heights and weight more concentrated about the mean.

The average height for boys in year 11 is;

152 + 177 + 181 + 172 + 162 + 155 + 169 + 168 + 179 + 158 + 182 + 196 + 165 + 194 + 150 + 168 + 165 + 168 + 162 + 192 + 184 + 167 + 157 + 163 + 173

25

= 170cm

 x x – 170 (x – 170)² 152 -18 324 177 7 49 181 11 121 172 2 4 162 -8 64 155 -15 225 169 -1 1 168 -1 1 179 9 81 158 -12 144 182 12 144 196 26 676 165 -5 25 194 24 576 150 -20 400 168 -2 4 165 -5 25 168 -2 4 162 -8 64 192 22 484 184 14 196 167 -3 9 157 -13 169 163 -7 49 173 3 9 Sum of standard deviations 3288

Conclusion

I think it was very important that I used random sampling to find the 25 boys and 25 girls for year 11 because this was the only way I could be sure my results would be fair and totally unbiased.

For year 11 boys I hypothesised that the taller you are the more you are to weigh, I decided to scatter graphs for just the boys and girls separately. This is because I thought that having separate graphs boys and girls separately gave stronger correlation and so therefore doing the mixed group would be a waste of time

For year 11 boys I found that there was strong positive correlation meaning that my hypothesis was correct. For girls there was weaker correlation than the boys.

For median, lower quartile, upper quartile there was never a difference of more than three, indicating that for height and weight boys and girls are very similarly match when It come to things like their interquartile range.

For the standard deviation of my results for year 11 boys and girls, I was sure that the girls would have smaller standard deviations then the boys. This is because boys tend to be taller and weigh a lot more then girls.

Overall I believe I have proved my hypothesis correct by proving boy weigh more then girls.

Suleman Farooq 10MWO

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.

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