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. The data is also discrete, quantitative data as the data can be used for calculations, and is discrete as you can only get set levels, such as level 6 and not level 6.4.

My raw data is on the following page; each year has been marked down, along with the number of students from each year group. The freak data can be seen along with all the other data.

Hypotheses.

1. I believe that the male’s modal group will be a higher level than the females.

2. I believe that the females will have a larger range of scores than males.

3. I believe that there may be stronger correlation between science and maths scores than there is with either subject with English.

4. I believe that over all three years the school’s results will have gotten better as a whole.

Sampling.

The method of sampling that I used is systematic sampling, as I chose every fifth member from each year and used their scores to do my calculations. However, I came across some difficulty as some of the students were either absent for one or more tests or had a result with which I could not work with. To get around this problem instead of using the freak data, I used the person nearest to them, with the same sex and then carried on using fifth members of the year.

This freak data is data, which is highly abnormal and if used in calculations will alter the end result dramatically. This is why I chose not to use them.

The reason why I chose to use systematic sampling was because I would be able to get an overall picture of what each year group achieved, without having to use every piece of data, which would have been very time consuming and would have entailed more calculations.

Tables of results.

- Average of levels over all three years and calculations.

This table shows the average number of people who achieved each level in each subject over all three years as well as the averages for male and female across the three years. I decided to combine the data over the three years in order to get an idea of their average scores so that I could compare them with what each year group achieved individually.

Science.

The mean level for females in science over all three years is: (X= level and f=frequency)

ΣfX÷Σf= (2x0+3x1+4x3+5x10+6x7+7x5+8x0) ÷(0+1+3+10+7+5+0)=5.46

The mean level is 5 for females in science over all.

The mean level for males in science over all three years is: ΣfX÷Σf= 5.56

The mean level is 6 for males in science over all.

The over all mean level for science over all three years is: ΣfX÷Σf= 5.46

The mean level is 5 over all three years for science.

The median level for females in science is: (number/s in the middle of the frequency of events if they were laid out ascending or descending)

Frequency= 26 Median=13th and 14th value (13th and 14th value=5 and 5)

Median= level 5

The median level for males in science is:

Frequency= 25 Median=13th value

Median= level 5

The median level for science over all three years is:

Frequency= 45 Median= 23rd value

Median= level 5

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

The modal level for males in science is: Mode= 5

The modal level in science over all three years is: Mode= 5

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

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

The range of levels in science over all three years is: Range= level 7-3= 4

Maths.

The mean level for females in maths over all three years is: ΣfX÷Σf= 5.46

The mean level is 5 for females in maths over all.

The mean level for males in maths over all three years is: ΣfX÷Σf= 5.59

The mean level is 6 for males in maths over all.

The over all mean level for maths over all three years is: ΣfX÷Σf= 5.35

The mean level is 5 over all three years for maths.

The median level for females in maths is:

Frequency= 27 Median= 13th value

Median= level 5

The median level for males in maths is:

Frequency= 22 Median= 11th and 12th values

Median= level 6

The median level for maths over all three years is:

Frequency= 42 Median= 21st and 22nd values

Median= level 5

The modal level for females in maths is: Mode= 5

The modal levels for males in maths is: Mode= 5 and 6

The modal level in maths over all three years is: Mode= 5

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

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

The range of levels in maths over all three years is: Range= 7-3= 4

English.

The mean level for females in English over all three years is: ΣfX÷Σf= 4.95

The mean level is 5 for females in English over all.

The mean level for males in English over all three years is: ΣfX÷Σf= 5.24

The mean level is 5 for males in English over all.

The over all mean level for English over all three years is: ΣfX÷Σf= 5.11

The mean level is 5 over all three years for English.

The median level for females in English is:

Frequency= 24 Median= 12th and 13th values

Median= level 5

The median level for males in English is:

Frequency= 25 Median= 13th values

Median= level 5

The median level for English over all three years is:

Frequency= 45 Median= 23rd values

Median= level 5

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

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

The modal level in English over all three years is: Mode= 5

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

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

The range of levels in English over all three years is: Range= 7-3= 4

- 1999 scores for female, male, the over all scores and calculations.

This table shows the results obtained by students who took the SATs exam in 1999. There are results for female, male and over all scores.

Science.

The mean level for females in science in 1999 is: (X= level and f=frequency)

ΣfX÷Σf= 5.17

The mean level is 5 for females in science in 1999.

The mean level for males in science in 1999 is: ΣfX÷Σf= 5.35

The mean level is 5 for males in science in 1999.

The over all mean level for science in 1999 is: ΣfX÷Σf= 5.46

The mean level is 5 in 1999 for science.

The median level for females in science in 1999 is:

Frequency= 28 Median= 14th and 15th values