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  • Level: GCSE
  • Subject: Maths
  • Word count: 3821

Mayfield igh Investigation

Extracts from this document...

Introduction

Mayfield High Handling Data Coursework Hypothesis I believe that the taller the person, the more they will weigh. This will be more visible in year 11, due to the rate of puberty. Also, boys in year 11 will mostly be taller than the girls, however in year 7 the heights will be more even or girls may even be taller due to their rate of puberty is at a lower age than boys. There should be a positive correlation between the weight and height of the pupils. Pre-test I will do a pre-test to ensure that my hypothesis will be correct. I will take a stratified sample from year 11 and then random sample the number of data needed for each gender and investigate the correlation between height and weight. I will then put this into a scatter graph which should then show a positive correlation between the weight and the height of the students. I have chosen year 11 above year 7 as the puberty rate will have slowed as the students approach adulthood, and the results should be clearer. I am selecting 40 students, and I will now work out how many girls and boys I will use. For year 11, there are 86 females (51% approx), and 84 males (49% approx) and 170 for the whole year. Year Sample number for year group Girls Boys 11 40 (86/170)*40=20.235 rounds to 20. (84/170)*40=19.76 rounds to 20. These are the random sample of the stratified sample in numerical order: Females: 2, 6, 7, 17, 20, 23, 24, 32, 33, 35, 36, 38, 55, 60, 64, 69, 72, 79, 81, 86 Males: 87, 88, 89, 90, 91, 95, 97, 98, 103, 105, 106, 111, 115, 123, 140, 161, 156, 164, 167, 170 Pre-test conclusion My graphs for my preliminary show that there is a positive correlation between weight and height, and that it is slightly different from females and males, as the males correlation is showing stronger than that of females. ...read more.

Middle

Cumulative Frequency graph A cumulative frequency graphs shows the total running frequency of the data in a graph, and allows you do plot where the median and inter-quartile ranges are. The line of best fit on the year 7 girl's cumulative frequency graph is flat and then all of a sudden steepens. This shows that after a certain point all the data is towards the higher end of my heights. This may suggest that some girls have not started puberty and not had their growth spurts, where as a lot of girls may have. Year 7 boys Heights (cm) Frequency Heights (cm) Cumulative frequency 135?h>140.5 2 135?h>140.5 2 140.5?h>145.5 3 140.5?h>145.5 5 145.5?h>-150.5 9 145.5?h>150.5 14 150.5?h>160.5 14 150.5?h>160.5 28 160.5?h>165.5 7 160.5?h>165.5 35 165.5?h>175 2 165.5?h>175 37 The modal class is 150.5?h>160.5 The median class is (37+1)/2=16 which means 150.5?h>160.5. Estimated mean: 5678.5/37=153.47 Heights (cm) 135?h>140.5 2 137.75 275.5 18975.0625 37950.125 140.5?h>145.5 3 142.5 427.5 20306.25 60918.75 145.5?h>150.5 9 147.5 1327.5 21756.25 195806.25 150.5?h>160.5 14 155 2170 24025 336350 160.5?h>165.5 7 162.5 1137.5 26406.25 184843.75 165.5?h>175 2 170.25 340.5 28985.0625 57970.125 Totals 37 5678.5 873839 Standard Deviation:= 7.96 cm The modal class and the median class are exactly the same as the year 7 girls. This may be because in year 7, girls and boys work at different puberty rates so the difference between them isn't as visible as in adults because the boys haven't started developing yet. However, the standard deviation is very different from the girls. As this one is much lower than the other, this suggests that the girls are more wide-spread due to puberty. As boys generally start puberty later, there is a much less variety to the outside data, which is why there is less of an average distance difference between each piece of the data. Scatter graph The graph shows a positive correlation as I predicted in my hypothesis. ...read more.

Conclusion

If I were to do it again, I may want to take 30 - 40 % of students from each year, instead of the initial 25 % I used. I would also include other years in my sample, so investigate how it would progress and possibly increase my variety of showing data, i.e. histograms and using spearmen's rank. I would also consider taking out more outliers to make sure my end results weren't skewed or anything by them and then maybe look at the data as a whole without grouping it first, to make it even more accurate. However, this is very time consuming. The approach I had in my hypothesis got supported the whole way through my findings - which height and weight had a positive correlation and that puberty affected the rates so that year 7 would be different to year 11 and that girls would be different to boys. I have found that the data I had suggests that the older you get, the more stable the heights and weights become, and they are not so all over the place and the clusters are tighter the older you get. I also found that the data suggests that in year 7 girls, there is a wider range compared to year 7 boys. This could be because of the puberty rates. By the time we get to the year 11 data, both girls and boys are pretty stable, of course there are some slightly off-the-cluster data, which is normal due to no human being is the same. All in all, what I have discovered is that my findings support my hypothesis, but if I were to investigate this again, I would do some things slightly differently, but some things I would keep very much the same - after all my data did support what I predicted in the first instance. ?? ?? ?? ?? ...read more.

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