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  • Level: GCSE
  • Subject: Maths
  • Word count: 7018

Statistics Mayfield High

Extracts from this document...

Introduction

Statistics / Data Handling Coursework                                Page  of

Statistics Coursework – Mayfield High School Database

This investigation is to analyze data in the Mayfield High School Database and come up with some hypothesis and to conclude whether there is reason to believe that they are true. I am going to investigate the data from Mayfield High is a database of information from the 1183 pupils at the school (when the database was compiled).

Hypothesis:

  1. Do Girls have a higher IQ than boys? It has often been said that girls do better at exams but does this mean that they have a higher IQ?
  1. Is there a correlation between the IQ and KS2 results? Often, those that have a high IQ have high levels in their KS2 results.
  1. Do those that watch more TV have a lesser IQ? Research has suggested that those who watch more TV have a lesser IQ but is this true at Mayfield?
  1. Is it true that the girls are taller than boys? Research has said that while boys may be stronger and heavier, Females are taller in general.

Any problem data will usually be removed. If there is no entry for the field, I will delete the entry. If there are any outliers, I will check whether it is 1.5 times greater than the Inter Quartile Range. If it is quite far away from the Lower Quartile or the Upper Quartile, I will discard the data but if it is not far away, I will decide on whether it should be omitted or not.

Some abbreviations I will use:

LQ = Lower Quartile

UQ = Upper Quartile

IQR = Inter Quartile Range

PMCC = Product Moment Correlation Coefficient

SD = Standard Deviation

KS2 = Key Stage 2

FD = Frequency Density

PMCC:                                         

              _ _

              Σxy - nx·y

r =  ____________________________

                 _          _

      √[ (Σx² - nx²)(Σy² - ny²) ]

image00.png

SD:                                                                                                 

image01.png

image12.pngimage15.png

Mean:                         of grouped data:

image14.png

image14.pngimage16.png = individual data

image17.png = number of values

image18.png= frequency

Normal Distribution:

image02.png

image02.png

...read more.

Middle

The Boys IQR is greater than that of the girls which suggests that the boys are more intelligent than the girls. This is supported by the higher median and IQR (as well as higher LQ and UQ). However, the girl’s outlier has a higher value than the two that the boys have and the girl’s highest value is greater than that of the boys. The girl’s whisker lengths are less clustered, suggesting that the girls are more intelligent than boys.

  • BW4

There are 200 pupils in Year 10: 96 are girls and 104 are boys:

 Girls = 96/200 x 50

         = 24

Therefore I will use 24 pieces of data from the girls.

min

79

LQ

93

78

=LQ - (1.5*IQR)

median

100

IQR

10

Outliers

15

UQ

103

118

=UQ + (1.5*IQR)

max

113

Boys = 104/200 x 50

         = 26

Therefore I will use 26 pieces of data from the boys.

min

78

LQ

90

69

=LQ - (1.5*IQR)

median

100

IQR

14

Outliers

21

UQ

104

125

=UQ + (1.5*IQR)

max

117

The minimum value for the girl’s box plot here is 79 and the maximum value is 113. The LQ is 93 and the UQ is 103; the IQR being 10. There is an outlier at either end: the low one being at 69 and the high one being at 120. The mean is 98.72 and the SD is 10.8. For the boy’s box plot, the lowest value is 78, the highest value being 117. The LQ is 90 and the 104; the IQR being 14 and the median being100. The mean is 98, the SD is 10.01 and there are no outliers.

The IQ’s of Year 10 girls and boys are very similar.  The median are exactly the same and there is little variation with the length of the whiskers – suggesting that neither gender is more intelligent than the other. Nevertheless, the girls have outliers (including a very low one) which leads to the conclusion that they are more intelligent in Year 10.

  • BW5

...read more.

Conclusion

1.35 ≤ x < 1.45                1.4        0.1        1        10

1.45 ≤ x < 1.55                1.5        0.1        9        90

1.55 ≤ x < 1.65                1.6        0.1        30        300

1.65 ≤ x < 1.75                1.7        0.1        9        90

1.75 ≤ x < 1.85                1.8        0.1        1        10

image14.png

The lower classes on the boys’ histogram have a fairly low FD compared to the higher classes. The modal class is 1.55 ≤ x < 1.65. The SD is 0.1168 and the mean is 1.642, which shows that the results are a bit skewed but fairly centred on the mean.

The female histogram has a normal distribution with a mean of 1.6 an SD of 0.0721, which shows that the results are very closely distributed around the mean. The modal class is, again, 1.55 ≤ x < 1.65, showing that the majority of the pupils have an average height.  The classes 1.45 ≤ x < 1.55 and 1.55 ≤ x < 1.65 are higher for girls than boys but the other three classes are lower: because the female histogram follows the normal distribution. Therefore, I believe that girls are taller than boys in general.

In Conclusion, I have been able to fully support 3 of my 4 hypothesis; my third hypothesis has been disproved.  Throughout my coursework I have used a range of calculations and graphs in the appropriate places which are useful and have supported my hypotheses to their full extent. I have hand drawn my Box and Whisker Plots because I have to hand draw some of them but also because it is much easier to do them by hand. There are some limits to my work because I had to sample some of my data. This was done for various reasons a few times, mainly to make my work easier to understand. The problem with sampling is that it does not give a full and fair representation of the population though the results may be the same as the un-sampled data; it is likely that is not as you do not use the entirety of the data available. Improvements could have been made to my hypotheses. I think that I have used all the best methods possible and used them to the best of my abilities.

Denis Twomey 10J                                      30/03/2008

...read more.

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