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Introduction

Maths Coursework Data Handling Task Statistics Data In this piece of coursework I have been set the task to find out about the students in our school. I need to prove the following hypothesis: 'Pupils in Band A perform better than pupils in Band B' I must suggest whether the hypothesis is correct or incorrect. I will do this by comparing Band A with Band B in the following areas: * Mean averages from key stage three- (level tiers 3-5, 4-6, 5-7) * Range of scores * Modal and median of the scores. There are many different techniques and methods which I can use to solve my above problem. I will use some techniques which will enable me to work out means, ranges, modes and medians of scores. To help me with my work I could also use cumulative frequency graphs, box plots and interquartile ranges. These will all help me to compare the differences between the two bands from looking at their scores. I am going to focus on 96 pieces of data (pupils) which I shall be analysing the levels and scores of both bands A and B. The first thing that I am going to do is, to compare the overall results from both bands regarding their scores from a maths SATS paper. This would involve me using a process called stratified sampling. This basically involves me reducing the amount of data that I need to compare. This method is seen as time consuming on a very large scale of data, which is handy for me. To compare the results I will need to sample the data. I am aiming to have a stratified sample size of 30 as it is nearly a third of my total data. Stratified sampling ensures that a fair proportion of pupils are chosen from both bands. I will use the maths levels data first, so now I need to find out how many pupils there are in each band. ...read more.

Middle

40 4 35 140 4 40 < s < 50 0 45 0 4 50 < s < 60 4 55 220 8 60 < s < 70 2 65 130 10 70 < s < 80 1 75 75 11 80 < s < 90 4 85 340 15 90 < s < 100 3 95 285 18 100 < s < 110 3 105 315 21 Total = 21 Total = 1505 Mean = 1505 = 71.6666......... 21 = 71.67 (2dp) Tier level 4-6 Maths Band A Score (s) Tally Frequency Mid-point Frequency * Mid-point Cumulative Frequency 0 < s < 10 0 5 0 0 10 < s < 20 0 15 0 0 20 < s < 30 0 25 0 0 30 < s < 40 0 35 0 0 40 < s < 50 0 45 0 0 50 < s < 60 0 55 0 0 60 < s < 70 1 65 65 1 70 < s < 80 0 75 0 1 80 < s < 90 5 85 425 6 90 < s < 100 2 95 190 8 Total = 8 Total = 680 Mean = 680 = 85 8 Band B Score (s) Tally Frequency Mid-point Frequency * Mid-point Cumulative Frequency 0 < s < 10 0 5 0 0 10 < s < 20 0 15 0 0 20 < s < 30 0 25 0 0 30 < s < 40 0 35 0 0 40 < s < 50 0 45 0 0 50 < s < 60 1 55 55 1 60 < s < 70 1 65 65 2 70 < s < 80 4 75 300 6 80 < s < 90 3 85 255 9 90 < s < 100 4 95 380 13 100 < s < 110 3 105 315 16 Total = 16 Total = 1370 Mean = 1370 = 85. ...read more.

Conclusion

I will look at each box plot for Band A and Band B under each tier (3-5, 4-6, 5-7). By looking at it this in this prospective it could show me things comparing the two in which I couldn't compare before like when I had frequency average tables where I could find the mean scores etc. with box plots it enables you to compare the median and interquartile of each Band. Tier 3-5 In the tier 3-5 Band A have performed slightly better than Band B. I say this because Band A has an interquartile of 52. This is only 2 more than Band B who had an interquartile of 50. So in this tier there is not a lot in between the two bands. They are basically really on even basis, whilst regarding this tier. Tier 4-6 In the tier 4-6 Band B have totally out performed Band A. there is a missive difference of around 14 in the two Bands interquartile. Band A interquartile is a minute 6 compared to that of Band B who has a interquartile of 20. Tier 5-7 In this certain tier again there is not a lot in it when contrasting the interquartile for both bands. In fact the difference is only the one and that in the favour of Band A. Band has got an interquartile of 17 compared to 16 of Band B. Overall for both Bands When comparing the overall interquartile for the two Bands it is difficult to separate them. Both Band A and Band B have the exact same interquartile as one another. Both bands managing to have a interquartile at 29. So by looking at the cumulative frequency graph and box plots to go with the overall tier section, it suggests that both performed as well as each other. If you were to look at the individual tiers Band A hand a upper hand on Band B. Band A had a better interquartile in two of the three tiers than Band B. Mathematics Coursework Balwant Singh Sandhu 10PT ...read more.

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