Data for each pupil was provided, such as name, age, year group, IQ, height, hair colour, eye colour, number of siblings, KS2 results, distance travelled between home and school, and gender. I have used gender, IQ, and KS2 results. From this I have drawn three scatter graphs.

Graph A: the results of both boys and girls

I predict that graph A will show positive, and relatively strong correlation. This shows that the higher the IQ, the higher the KS2 result and the lower the IQ, the lower the KS2 result.

Graph A shows relatively strong, and positive correlation. This suggests that the higher the IQ, the higher the KS2 results. The KS2 results range from 3 to 5 and are evenly spread. However, because there are only a few possible Key Stage results, of which the most you can get 3 separate results. So, by choosing to do an average I have increased the amount of places the points can be plotted, and it is more accurate. Also a lot of the results were the same and this makes the line of best fit harder to plot. From the line of best fit I worked out the gradient by:

## Difference in y / Difference in x = 7/0.45 =15.5555555

The gradient is 15.6, showing that the IQ and KS2 results are not in direct proportion. From the line of best fit I can also find out what the y intercept is, and considering x represents average KS2 results and y represents IQ, I worked out as below:

Y=mx+c

89=3.5m+c 1

97=4m+c 2

2-1

8 =0.5m

0.5 0.5

16=m

Substitute:

97=16x4+c

97=64+c

(-64) (-64)

33=c

From this I can predict that a person with an IQ of 110 got an average KS2 result of 4.81 (3sf)

There will be better correlation between IQ and KS2 results if I consider boys and girls separately. The scatter graphs will use the same data but only girls will be plotted on one graph, and boys on the other.

Graph B: the boys and girls plotted separately

They are plotted separately on one axis so as to compare them easily. The lines of best fit are also shown, the boys are in blue and the girls are in pink.

I predict that both will show stronger, positive correlation. However, the lines of best fit will differ, as the results for each vary. I think the boys will have clustered results and their results will be lower than the girls, their highest mark being 5 and the girls’ highest mark being 5.3. I think that the girls will have the steepest gradient, and the lines of best fit will cross because the girls vary from one extreme to the other.

The boys’ results show stronger, positive correlation. The boys have much of the same result between a range in IQ, as between the IQ’s of 97 and 101; they have all achieved level 4. This perhaps shows that the results can be analysed more thoroughly if in points instead of levels. For instance, if the results were out of 100, and the mark was 50, the level may be 3, although 10 marks higher than the boundary. So, I believe that although they achieved the same result, the higher the IQ, the higher the amount of points would have been.

The gradient is 18, and so it is not in direct proportion, it is also steeper than that of the girls, due to the highest and lowest result. This shows that if they have an IQ of 110, they will achieve less than the girls. However, if the boys have an IQ of 50, they will achieve higher than the girls. Showing the graph is not accurate enough, and so I must do further investigation. The y intercept is 25. From this I can predict that a boy with an IQ of 100 will get an average KS2 result of 4.17 (3sf).

The girls’ results show stronger, positive correlation. The gradient is 15.3, and so it is not in direct proportion, and the intercept is 34.8. From this I can predict that a girl with an IQ of 100 will get an average KS2 result of 4.26 (3sf).

The lines of best fit, from boys and girls, cross, showing that the boys have an average IQ and result, and the girls pass from one extreme to the other.

In conclusion, from these graphs I have found that the higher the IQ, the higher the KS2 result. Also, when the girls’ IQ is above 97, they will achieve a higher result than the boys. However, when their IQ is below 97, they will achieve a lower result than the boys.

The lines of best fit are the best judgment between IQ and KS2 results. There are exceptional values (such as the boy with the IQ of 96 achieved the KS2 result 3.3), which fall outside the line of best fit.

Graph C: girls’ results in cumulative frequency curve or ogive

I took the data used for the scatter graph and filled in the table below:

I predict that the girls will have a median result close to the upper quartile range because the KS2 results are mainly high. This is because most girls have KS2 results between 3.5 and 4.5, making the median higher.

In graph C my hypothesis is proven to be correct and I can show this with a box and whisker plot.

From this range of results, the lower quartile range, the upper quartile range and the median can be seen clearly.

Graph D: boys’ results in cumulative frequency curve or ogive

I took the data from my scatter graph to fill in the following table:

I predict that the median will be closer to the lower quartile, however, from the scatter graph we can see the boys’ results are well spaced, and so the lower and upper quartile range will probably be equally spaced. I also think because the boys were well spaced, their upper and lower quartile range will be higher than the girls, but their median will be lower.

In graph D my hypothesis was proven to be correct and I can show this with a box and whisker plot:

This shows the upper and lower quartile ranges to be higher than the girls but their median is lower, and so they will achieve less than the girls. Thus, showing that girls are more intelligent than boys.

I conclude that the higher the IQ, the higher the result. Also that girls are more intelligent than boys. This is concluded mainly from the ogive because the girls have a higher percentage achieving level 5 than boys do.

17.5 x 100 = 87.5% = girls

20

16.5 x 100 = 80.75% = boys

20

87.5-80.75=6.75%

6.75% more girls achieve level 5 than boys. This does not mean that girls are generally more intelligent, because at a lower IQ, boys will achieve higher than girls.

There is positive correlation between IQ and KS2 results in every one of the scatter graphs, showing that the higher the IQ, the higher the KS2 result.

The points on the scatter graphs are not very dispersed, and so it is not as accurate as it could be. However, the correlation is better when the girls and boys are separated, than when they are put together, suggesting that in future I should plot separate graphs for both boys and girls.

The scatter graphs can be used to give reasonable predictions of KS2 results and IQ by either reading from the graph or using y=mx+c

Cumulative frequency curves confirm that when girls have an IQ above 97, they are more intelligent than boys. When they have an IQ that is below 97, they are not as intelligent as boys.

The median for the girls is higher than that of the boys.

From the box and whisker plots I can conclude that girls are more intelligent than boys, and can be used to estimate that6.75% more girls achieve level 5 than boys.

My analysis would have been more accurate had I have taken larger samples, and specified the years in which the students were in, using separate graphs for each year and gender.

My predictions are based on general lines of best fit and do not take into account the exceptional points.

A sample of 40 students was taken, 20 boys and 20 girls, and I have found that IQ and Key Stage 2 results do have a relationship and that the higher the IQ, the higher the result. Also, that, girls are more intelligent than boys at a higher IQ, but are less intelligent than boys at a lower IQ.

If I carried on researching into this, factors I would compare are: Age, Gender, Race, Social background, Amount of days absent, Parents IQ, Single parents, and Siblings

The factor that dominated was gender and I took this into account when investigating.