Median= level 5 and 6
The median level for males in science in 1999 is:
Frequency= 26 Median=13th and 14th values
Median= level 5
The median level for science in 1999 is:
Frequency= 54 Median= 27th and 28th values
Median= level 5
The modal level for females in science in1999 is: (the level which was achieved by most people). Mode= 5
The modal level for males in science in 1999 is: Mode= 6
The modal level in science in 1999 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 in 1999 is: Range= level 7-3= 4
The range of levels in science in 1999 is: Range= level 7-3= 4
Maths.
The mean level for females in maths in 1999 is: ΣfX÷Σf= 5.07
The mean level is 5 for females in maths in 1999.
The mean level for males in maths in 1999 is: ΣfX÷Σf= 5.73
The mean level is 6 for males in maths in 1999.
The over all mean level for maths in 1999 is: ΣfX÷Σf= 5.75
The mean level is 6 for maths in 1999.
The median level for females in maths in 1999 is:
Frequency= 28 Median= 14th and 15th values
Median= level 5
The median level for males in maths in 1999 is:
Frequency= 26 Median=13th and 14th values
Median= level 5
The median level for maths in 1999 is:
Frequency= 54 Median= 27th and 28th values
Median= level 5
The modal level for females in maths in 1999 is: Mode= 4
The modal levels for males in maths in 1999 is: Mode= 6
The modal level in maths in 1999 is: Mode= 6
The range of levels for females in maths in 1999 is: Range= 7-3= 4
The range of levels for males in maths in 1999 is: Range= 7-3= 4
The range of levels in maths in 1999 is: Range= 7-3= 4
English.
The mean level for females in English in 1999 is: ΣfX÷Σf= 4.89
The mean level is 5 for females in English in 1999.
The mean level for males in English in 1999 is: ΣfX÷Σf= 5.04
The mean level is 5 for males in English in 1999.
The in 1999mean level for English in 1999 is: ΣfX÷Σf= 5.15
The mean level is 5 in 1999 for English.
The median level for females in English in 1999 is:
Frequency= 28 Median= 14th and 15th values
Median= level 5
The median level for males in English in 1999 is:
Frequency= 26 Median=13th and 14th values
Median= level 5
The median level for English in 1999 is:
Frequency= 54 Median= 27th and 28th values
Median= level 5
The modal level for females in English in 1999 is: Mode= 4
The modal levels for males in English in 1999 is: Mode= 5
The modal level in English in 1999 is: Mode= 5
The range of levels for females in English in 1999 is: Range= 7-3= 4
The range of levels for males in English in 1999 is: Range= 7-3= 4
The range of levels in English in 1999 is: Range= 7-3= 4
- 2000 scores for female, male, the over all scores and calculations.
This table shows the results obtained by students who took the SATs exam in 2000. There are results for female, male and over all scores.
Science.
The mean level for females in science in 2000 is: (X= level and f=frequency)
ΣfX÷Σf= 5.05
The mean level is 5 for females in science in 2000.
The mean level for males in science in 2000 is: ΣfX÷Σf= 5.90
The mean level is 6 for males in science in 2000.
The over all mean level for science in 2000 is: ΣfX÷Σf= 5.45
The mean level is 5 in 2000 for science.
The median level for females in science in 2000 is:
Frequency= 20 Median=10th and 11th values
Median= level 5
The median level for males in science in 2000 is:
Frequency= 21 Median= 11th value
Median= level 5
The median level for science in 2000 is:
Frequency= 41 Median= 21st value
Median= level 5
The modal level for females in science in 2000 is: (the level which was achieved by most people). Mode= 6
The modal level for males in science in 2000 is: Mode= 5
The modal level in science in 2000 is: Mode= 5
The range of levels for females in science in 2000 is: Range= level 7-3= 4
The range of levels for males in science in 2000 is: Range= level 7-5= 2
The range of levels in science in 2000 is: Range= level 7-3= 4
Maths.
The mean level for females in maths in 2000 is: ΣfX÷Σf= 5.45
The mean level is 5 for females in maths in 2000.
The mean level for males in maths in 2000 is: ΣfX÷Σf= 5.33
The mean level is 5 for males in maths in 2000.
The over all mean level for maths in 2000 is: ΣfX÷Σf= 5.39
The mean level is 5 for maths in 2000.
The median level for females in maths in 2000 is:
Frequency= 20 Median=10th and 11th values
Median= level 5
The median level for males in maths in 2000 is:
Frequency= 21 Median= 11th value
Median= level 5
The median level for maths in 2000 is:
Frequency= 41 Median= 21st value
Median= level 5
The modal level for females in maths in 2000 is: Mode= 6
The modal levels for males in maths in 2000 is: Mode= 5
The modal level in maths in 2000 is: Mode= 5
The range of levels for females in maths in 2000 is: Range= 6-4= 2
The range of levels for males in maths in 2000 is: Range= 7-3= 4
The range of levels in maths in 2000 is: Range= 7-3= 4
English.
The mean level for females in English in 2000 is: ΣfX÷Σf= 4.65
The mean level is 5 for females in English in 2000.
The mean level for males in English in 2000 is: ΣfX÷Σf= 4.57
The mean level is 5 for males in English in 2000.
The mean level for English in 2000 is: ΣfX÷Σf= 5.12
The mean level is 5 in 2000 for English.
The median level for females in English in 2000 is:
Frequency= 20 Median=10th and 11th values
Median= level 5
The median level for males in English in 2000 is:
Frequency= 21 Median= 11th value
Median= level 5
The median level for English in 2000 is:
Frequency= 41 Median= 21st value
Median= level 5
The modal level for females in English in 2000 is: Mode= 5
The modal levels for males in English in 2000 is: Mode= 5
The modal level in English in 2000 is: Mode= 5
The range of levels for females in English in 2000 is: Range= 6-2= 4
The range of levels for males in English in 2000 is: Range= 7-4= 3
The range of levels in English in 2000 is: Range= 7-2= 5
- 2001 scores for female, male, the over all scores and calculations.
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.
- Over all three years, for science and maths for females. (Working for Co-efficient of rank correlation)
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
- Over all three years, for science and maths for males. (Working for Co-efficient of rank correlation)
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
-
Over all three years for science and maths for both males and females. (Working for Co-efficient of rank correlation)
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)
Σ D² = 8.5
1-(6xΣ D²) ÷ n(n²-1)
1-(6x8.5) ÷ 7(7²-1)
1- 51 ÷ 336
- 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
- Over all three years, for science and English for males. (Working for Co-efficient of rank correlation)
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
-
Over all three years for science and English for both males and females. (Working for Co-efficient of rank correlation)
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)
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
- Over all three years, for maths and English for males. (Working for Co-efficient of rank correlation)
Σ D² = 9
1-(6xΣ D²) ÷ n(n²-1)
1-(6x9) ÷ 7(7²-1)
1-54 ÷ 336
1- 0.16 = 0.84
There is good correlation between male maths 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 0.84 1
-
Over all three years for maths and English for both males and females. (Working for Co-efficient of rank correlation)
Σ D² = 8
1-(6xΣ D²) ÷ n(n²-1)
1-(6x8) ÷ 7(7²-1)
1- 48 ÷ 336
1- 0.14 = 0.86
There is good correlation between both sex’s maths and English scores. However, the correlation is not as strong as the correlation between both sex’s science and maths levels, it is quite a bit off.
Good negative No Good
Correlation Correlation Correlation
-1 0 0.86 1
I decided to look at the correlation as one of my hypotheses is “I believe that there may be stronger correlation between science and maths scores than there is with either subject with English”. By finding out the co-efficient of rank correlation I was able to see whether or not my hypothesis was correct. By finding the correlation between subjects I am able to see whether or not they are linked, for example people often say that maths is linked to science. Finding the correlation between these
subjects allows me to see whether or not those who do well in one do well in another and therefore whether or not they support this theory.
Science.
Here are some comparative bar charts, showing science results for all three years and the average results over all three years.
Looking at the bar charts you can see that as the three years have gone females have achieved lower results than before in the past. Most females are achieving between levels 4-6, whereas before they were achieving levels 5-7 more frequently.
Males are achieving higher grades also, such as more level 6’s and 7’s and less level 4’s than before. Males too are achieving a larger amount of level 3’s than in 1999, however, they make up for this by achieving more higher levels than before. Males seem to be achieving more consistently throughout the years compared to the females.
There are more male and female students who are achieving level 3 than in 1999, when none achieved this level. For females the three most commonly achieved levels do not have as much difference between the other levels as the difference between the males three most commonly achieved levels, which are much more distinguishable from the achieved other levels. Also more females achieve the mean level over all for science, however, more males than females achieve higher levels in science over all.
Maths.
Here are some comparative bar charts, showing maths results for all three years and the average results over all three years.
Looking at the bar charts you can see that as the three years have gone females have achieved more level threes than in 1999 and 2000, however, they are achieving slightly better in levels 5 and 6. Fewer females are achieving level 7 than in 1999.In 1999 the scores were more spread evenly across the levels, but in the latter years they are scoring respectable higher in levels 5 and 6 than any other level. However, females scored levels 3’s in 2001, which they had never done before in the past two years, they also scored level 8’s, which also has never been done before.
Males appear to be getting worse at maths, in 1999 more males were achieving levels 6 and 7 compared to females. Then in later years males achieve less level 5’s and 6’s than females. However, males still score quite closely to the females and males achieve more level 7’s than the females. Males seem to be achieving quite consistent levels throughout the years.
Fewer females achieve the mean level over all three years for maths; both sexes achieve more or less the same amount of level 6’s and 7’s.
English.
Here are some comparative bar charts, showing English results for all three years and the average results over all three years.
Looking at the bar charts you can see that as the three years have gone females have achieved more level threes than in 1999 and 2000, however, they are achieving higher in levels 5 and 6. Fewer females are achieving level 7 than in 1999.In 1999 the scores were more spread evenly across the levels, but in the latter years they are scoring respectable higher in levels 5 and 6. However, females scored levels 2’s in 2000, which they had never done. It seems that females are getting better at English over the three years than the males, as in 1999 males scored much higher level 5, but now females are scoring higher in almost all levels, especially level 5.
Males appear to be getting worse at English; in 1999 more males were achieving level 5’s compared to females. Then in later years males achieve less level 5’s and 6’s than females. Male’s scores seem to be grouping between levels 4-7, whereas female’s scores are all over the spectrum.
Fewer females achieve the mean level over all three years for maths and also they achieve less level 6’s and 7’s over all, achieving many more level 3’s than the males.
Cumulative frequency graphs.
I decided to put the over all data for each subject onto cumulative frequency graphs; I decided to do this as it is easy to extract certain data such as the median from the graph. It is also easy to remove what can be called freak data, which is extreme data and is at either end of the scale.
I decided to find the median for each subject so that I could compare them to each other. By using the 1rst and 9th deciles I was able to cut out any freak data, which could be very extreme and once again it aids comparison between the subjects. The interquartile range shows the middle half of the data and disallows any freak data. This shows what most of the people are achieving in terms of their SATs levels.
Box and whisker diagrams.
Here are three box and whisker diagrams, which are showing the medians, interquartile ranges and overall ranges of all the subjects over the three years from which this data was collected.
As you can see from the box and whisker diagrams the medians for science and maths are almost the same. However, the median for English is quite a bit lower. The interquartile ranges of maths and science are also almost identical, whereas the interquartile range for English is considerably lower. This shows that the science and maths scores have more in common than either subject with English and that people are achieving roughly the same scores in science and maths. The overall range for all three subjects is almost the same in every case, although maths does go one level higher than English and science. This simply shows that people are able to achieve higher in math than in the other two subjects, it also means that people are achieving a more varied range of scores in maths than in the other subjects.
I decided to use box and whisker diagrams as they show the data more clearly than a cumulative frequency graph does, also it is easier to compare the data in box and whisker diagrams. This is as you can put the diagrams one above the other as I have done and see how the medians, interquartile ranges and ranges differ with ease.
Averages.
Here are some comparative bar charts, showing all three subject’s results as averages over all three years.
Pie Charts.
I decided not to do comparative pie charts, as the numbers produced would not have enlarged the area, but made it smaller. Instead I decided to use a normal pie chart to show the percentage of each gender and year groups SATs levels. I think that this is a better way than using comparative pie charts as you can compare them easier. It is obvious at a glance, which gender is achieving which results and how many in comparison to the percentage achieved by the other years and gender.
Science.
Results over all three years.
360 ÷ 26= 13.8 360 ÷ 25=14.4
Degrees= 360 ÷ Σn
Results for 1999
360 ÷ 26= 13.8
Results for 2000
360 ÷ 20= 18 360 ÷ 21= 17.1
Results for 2001
360 ÷ 25= 14.4 360 ÷ 20= 18
English
Results over all three years.
360 ÷ 24= 15 360 ÷ 25=14.4
Degrees= 360 ÷ Σn
Results for 1999
360 ÷ 26= 13.8
Results for 2000
360 ÷ 20= 18 360 ÷ 21= 17.1
Results for 2001
360 ÷ 25= 14.4 360 ÷ 20= 18
Maths.
Results over all three years.
360 ÷ 27= 13.3 360 ÷ 22= 16.4
Degrees= 360 ÷ Σn
Results for 1999
360 ÷ 26= 13.8
Results for 2000
360 ÷ 20= 18 360 ÷ 21= 17.1
Results for 2001
360 ÷ 25= 14.4 360 ÷ 20= 18
Interpretation and conclusion.
These were my 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.
As I worked with the data, and showed my results I began to see that some of my hypotheses were correct and others only partially correct. My findings were that there is better correlation between maths and science than any other two subjects, the range of females levels were higher than that of the males, the median and mean levels for both genders overall were basically the same, the ranges were almost identical and the modal groups on a whole were also the same.
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.
