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  • Level: GCSE
  • Subject: Maths
  • Word count: 7646

Comparison of SATs results to obtain statistical data on students.

Extracts from this document...

Introduction

Hanna Cheung

Comparison of SATs results to obtain statistical data on students.

Introduction.

I have chosen to look at the school’s SATs scores for the past three years. I decided to choose this topic as I felt hat it would be interesting to compare the results, also I thought that the topic would give me some good data to work with.

        I thought that it could be possible to compare scores between sexes, if the scores on average have changed either better or worse. As well, I thought that it would be interesting to see if there is any correlation between subjects and their scores.

Data.

The data that I am using is past SATs scores from the schools records, over three years. I decided to use three sets of data so I can compare several years of results, this will enable me to get average scores over all three years for both male and female and also an average of all scores, using three years worth of data will also allow me to have more data to work with.  

I think that the way in which I got my data, which was taking them straight from the school’s records, is best because many students would not know/remember their scores; I can receive as much data from each year as I want without much hassle or time wasted. Also this way eliminates the possibility that the data that I received is false, as students may wish to say that they got better or worse scores than they actually did.

The data that I am using is secondary data, as I did not receive it from the students themselves, which would be primary data.

...read more.

Middle

18

10

4

0

This table shows the results obtained by students who took the SATs exam in 2001. There are results for female, male and over all scores.

Science.

The mean level for females in science in 2001 is: (X= level and f=frequency)

ΣfX÷Σf= 5.36

The mean level is 5 for females in science in 2001.

The mean level for males in science in 2001 is: ΣfX÷Σf= 5.55

The mean level is 6 for males in science in 2001.

The over all mean level for science in 2001 is: ΣfX÷Σf= 5.43

The mean level is 5 in 2001 for science in 2001.

The median level for females in science in 2001 is:

Frequency= 25        Median= 13th value

Median= level 5

The median level for males in science in 2001 is:

Frequency= 20        Median= 10th and 11th value        

Median= level 6

The median level for science in 2001 is:

Frequency= 45        Median= 23rd and 24th values

Median= level 5

The modal level for females in science in2001 is: (the level which was achieved by most people). Mode= 5

The modal level for males in science in 2001 is: Mode= 6

The modal level in science in 2001 is: Mode= 6

The range of levels for females in science in 20001 is: Range= level 7-3= 4

The range of levels for males in science in 2001 is: Range= level 7-3= 4

The range of levels in science in 2001 is: Range= level 7-3= 4

Maths.

The mean level for females in maths in 2001 is: ΣfX÷Σf= 4.72

The mean level is 5 for females in maths in 2001.

The mean level for males in maths in 2001 is: ΣfX÷Σf= 5.55

The mean level is 6 for males in maths in 2001.

The over all mean level for maths in 2001 is: ΣfX÷Σf= 5.09

The mean level is 5 for maths in 2001.

The median level for females in maths in 2001 is:

Frequency= 25        Median= 13th value

Median= level 5

The median level for males in maths in 2001 is:

Frequency= 20        Median= 10th and 11th value        

Median= level 6

The median level for maths in 2001 is:

Frequency= 45        Median= 23rd and 24th values

Median= level 6

The modal level for females in maths in 2001 is: Mode= 6

The modal levels for males in maths in 2001 is: Mode= 6

The modal level in maths in 2001 is: Mode= 6

The range of levels for females in maths in 2001 is: Range= 8-3= 5

The range of levels for males in maths in 2001 is: Range= 7-3= 4

The range of levels in maths in 2001 is: Range= 8-3= 5

English.

The mean level for females in English in 2001 is: ΣfX÷Σf= 5.8

The mean level is 6 for females in English in 2001.

The mean level for males in English in 2001 is: ΣfX÷Σf= 5.05

The mean level is 5 for males in English in 2001.        

The in 2001mean level for English in 2001 is: ΣfX÷Σf= 5.07

The mean level is 5 in 2001 for English.

The median level for females in English in 2001 is:

Frequency= 25        Median= 13th value

Median= level 5

The median level for males in English in 2001 is:

Frequency= 20        Median= 10th and 11th value        

Median= level 5

The median level for English in 2001 is:

Frequency= 45        Median= 23rd and 24th values

Median= level 5

The modal level for females in English in 2001 is: Mode= 5

The modal levels for males in English in 2001 is: Mode= 4and 5

The modal level in English in 2001 is: Mode= 5

The range of levels for females in English in 2001 is: Range= 7-3= 4

The range of levels for males in English in 2001 is: Range= 7-4= 3

The range of levels in English in 2001 is: Range= 7-3= 4

The reason why I chose to find the mean levels for each of the year groups overall and for both the females and males was so that I could compare what level on average each of the genders were achieving. The mean shows me the average level achieved. By finding the mean for every year, all 3 years combined and for both sexes in every year I was able to see which sex was on average better at which subjects and whether or not either gender had improved over the years.

I chose to find the median levels achieved because the median shows the middle value, this means that the median level is the ‘normal’ level. I can look at the median levels for all three years and compare them to one another to see whether or not my hypotheses are correct.

I found the modal level because it showed me, which level was being achieved by the largest amount of people in each gender and year. This shows me whether or not females are achieving more, higher grades than males and vice versa.

I decided to find the range of levels using the data on SATs scores as one of my hypotheses is “I believe that the females will have a larger range of scores than males”. By finding the range I was able to see whether or not my hypothesis is correct.

Graphs.

  1. Over all three years, for science and maths for females. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Science

0 6.5

1 5

3 4

10 1

7 2

5 3

0 6.5

Maths

0 7

1 5.5

6 3

7 2

9 1

3 4

1 5.5

Difference

0.5

0.5

1

1

1

1

1

Difference²

0.25

0.25

1

1

1

1

1

Σ D² = (0.25+0.25+1+1+1+1+1) 4.5

1-(6xΣ D²) ÷ n(n²-1)

1-(6x4.5) ÷ 7(7²-1)

1-27 ÷ 336

1-0.08 = 0.92

There is good correlation between female science and maths over all.

Good negative                                No                                                Good        

Correlation                              Correlation                                        Correlation

_____________________________________________________________________________

-1                                                0                                                 0.92          1

  1. Over all three years, for science and maths for males. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Science

0 6.5

1 5

2 4

9 1

8 2

5 3

0 6.5

Maths

0 6.5

1 4.5

1 4.5

8 1.5

8 1.5

4 3

0 6.5

Difference

0

0.5

0.5

0.5

0.5

0

0

Difference²

0

0.25

0.25

0.25

0.25

0

0

Σ D² = 2

1-(6xΣ D²) ÷ n(n²-1)

1-(6x2) ÷ 7(7²-1)

1-12 ÷ 336

1- 0.04 = 0.96

There is very good correlation between male science and maths over all, even better than the correlation between female science and maths over all three years.

Good negative                                No                                                Good        

Correlation                              Correlation                                        Correlation

-1                                                0                                                           0.96    1

  1. Over all three years for science and maths for both males and females. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Science

0 6.5

2 5

5 4

19 1

15 2

10 3

0 6.5

Maths

0 7

2 5

7 3.5

15 2

17 1

7 3.5

1 6

Difference

0.5

0

0.5

1

1

0.5

0.5

Difference²

0.25

0

0.25

1

1

0.25

0.25

Σ D² = 3

1-(6xΣ D²) ÷ n(n²-1)

1-(6x3) ÷ 7(7²-1)

1-18 ÷ 336

1- 0.05 = 0.95

There is very good correlation between both sexes science and maths scores. The correlation over all is closer to the male correlation than the female.

Good negative                                No                                                Good        

Correlation                              Correlation                                        Correlation

-1                                                0                                                        0.95       1

Over all three years for science and English for females. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Science

0 6.5

1 5

3 4

10 1

7 2

5 3

0 6.5

English

0 6.5

2 4.5

5 2

11 1

4 3

2 4.5

0 5.5

Difference

0

0.5

2

0

1

1.5

1

Difference²

0

0.25

4

0

1

2.25

1

Σ D² = 8.5

1-(6xΣ D²) ÷ n(n²-1)

1-(6x8.5) ÷ 7(7²-1)

1- 51 ÷ 336

  1. 0.15 = 0.85

There is good correlation between science and English scores. However, this correlation is not as good as the female correlation between science and maths scores.

Good negative                                No                                                Good        

Correlation                              Correlation                                        Correlation

-1                                                0                                        0.85                       1

  1. Over all three years, for science and English for males. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Science

0 6.5

1 5

2 4

9 1

8 2

5 3

0 6.5

English

0 6

0 6

5 2.5

12 1

5 2.5

3 4

0 6

Difference

0.5

1

1.5

0

0.5

1

0.5

Difference²

0.25

1

2.25

0

0.25

1

0.25

Σ D² = 5

1-(6xΣ D²) ÷ n(n²-1)

1-(6x5) ÷ 7(7²-1)

1-30 ÷ 336

1- 0.09 = 0.91

There is good correlation between male science and English over all, but once again it is not as strong a correlation compared to the male science and maths correlation.

Good negative                                No                                                Good        

Correlation                              Correlation                                        Correlation

-1                                                0                                                 0.91              1

  1. Over all three years for science and English for both males and females. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Science

0 6.5

2 5

5 4

19 1

15 2

10 3

0 6.5

English

0 6.5

2 5

10 2

33 1

9 3

5 4

0 6.5

Difference

0

0

2

0

1

1

0

Difference²

0

0

4

0

1

1

0

Σ D² = 6

1-(6xΣ D²) ÷ n(n²-1)

1-(6x6) ÷ 7(7²-1)

1- 36 ÷ 336

1- 0.11 = 0.89

There is good correlation between both sex’s science and English scores. The correlation is not as strong as the correlation between both sexes science and maths, it is quite a bit off.

Good negative                                No                                                Good        

Correlation                              Correlation                                        Correlation

-1                                                0                                               0.89                1

7. Over all three years for maths and English for females. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Maths

0 6.5

1 5

3 4

10 1

7 2

5 3

0 6.5

English

0 7

1 5.5

6 3

7 2

9 1

3 4

1 5.5

Difference

0.5

0.5

1

1

1

1

1

Difference²

0.25

0.25

1

1

1

1

1

Σ D² = 5.5

1-(6xΣ D²) ÷ n(n²-1)

1-(6x5.5) ÷ 7(7²-1)

1- 33 ÷ 336

1- 0.10 = 0.90

There is good correlation between maths and English scores. However, although it is close to that of the female’s, the correlation is not quite as good.

Good negative                                No                                                Good        

Correlation                              Correlation                                        Correlation

    -1                                                0                                                0.90               1

  1. Over all three years, for maths and English for males. (Working for Co-efficient of rank correlation)

Levels

2

3

4

5

6

7

8

Maths

0 6.5

1 4.5

1 4.5

8 1.5

8 1.5

4 3

0 6.5

English

0 6

0 6

5 2.5

12 1

5 2.5

3 4

0 6

Differe ...read more.

Conclusion

In some subjects both males and females modal groups were higher than the opposite gender, but on a whole they were the same. This went against hypothesis no. 1. I believed that the modal group for males would have been higher as I suspected that females would be achieving levels all over the spectrum. However, overall males only had one higher modal group and this was in maths where they had two modal groups of levels 5 and 6 whereas the female’s modal group was level 5.

Only in one subject did the females have a larger range of scores than the males, but for a different subject the males had a larger range of scores than the females, which was not as suspected.

It seems that on a whole males are achieving worse in their maths and English over the years. However, they seem to be getting better or at least maintaining their aptitude with science. Female’s

scores in maths and English have actually gotten slightly better but also worse and in science they are not achieving as highly as they did before. Overall the students seem to not be achieving better and better as I believed they would have through my hypothesis.

There was indeed stronger correlation between maths and science, for both sexes than for any two other subjects. However, the correlation was not that much stronger than the correlation between any other two subjects.

On a whole the schools results did not get better as I had anticipated, in fact they got slightly worse, especially the females.

...read more.

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