I am investigating to find a relationship between ks2 results and IQ in children and to determine whether there is a significant difference between boys and girl's ks2 results and IQ.

When I had chose how many boys and girls are taken from each year, I got a random sample of people by using my random number generator on my calculator so it would rule out any bias that I may have. Each person is numbered so we put into the calculator how many people there are that are male for year 7 and we picked 12 boys at random. We did this for boys and girls according to the proportion of people in each year. I then sorted this data into groups of years and sex. I will then work out the KS2 total level so that it is easier to compare and with the other ks2 results.

Planning

I am going to do the following calculations: mean and standard deviation for boy's, girl's and the whole sample IQ and ks2 scores from the data that I have collected. Also I will need to find the range, inter-quartile range, and spearman's coefficient of rank correlation?????. I will show some of this information in the following diagrams: 2 back to back stem and leaf, one for the whole ks2 results, one for the whole IQ scores, 2 box and whisker, one showing boys and girls IQ score, one showing boys and girls ks2 results and three scatter diagrams one for the boys IQ and ks2 scores, one for the girls IQ and ks2 scores and one for the whole sample IQ and ks2 scores.

I will use a stem and leaf diagram for an instant comparison and it will show the basic shape of distribution and a box and whisker diagram to show who are more intelligent between boys and girls.

I will work out the median for the IQ and ks2 results for boys and girls because it is needed in the Box and whisker diagrams. They are used for looking inside of the inter-quartile range and seeing where the median is in it.

I am using the mean, standard deviation, and median to compare the results between boys and girls IQ and ks2 results. I am using standard deviation to measure the spread of results around the mean this is useful because it rules out any extreme values. These calculations will be useful because they will show the relationship between boys and girls. The standard deviation shows ho close the boys and girls are to the mean.

I will use the scatter diagram to directly answer both statements, which are to determine whether there is a difference between the boys and girl's ks2 results and IQ. Also to confirm whether there is a relationship between a person's IQ and ks2 results. These diagrams will help me show a relationship between IQ and Ks2 results and the relationship between boys and girls. As a result of these calculations and diagrams I will be able to compare the ks2 results and IQ in children and to see whether there is a relationship between boys and girls.

I will use Spearman's coefficient of rank correlation to show how strong the correlation is between boy's ks2 results and IQ, girl's ks2 results and IQ and the whole sample of ks2 results and IQ.

Interpretation

My calculations will help me to investigate whether there is a relationship between ks2 results and IQ in children and to discover whether there is a significant difference between boys and girls. This will help me suggest my hypothesis is true, which is that there is a relationship between IQ and ks2 result and there is a difference in intelligence between boys and girls.

The girls ks2 results are evenly spread this shows that within the inter-quartile range it is an even spread, for the boys is positively skewed which means that most of the results within the inter-quartile range are higher than the median. A quarter of the boys results are between 11 and 12 but the next quarter are much more spread out between 12 and 15 this diagram reinstates the point that the results of the boys are less consistent than the girls.

The inter-quartile range for boys IQ scores has a smaller range than the girls, this shows that the girls are less consistent close to the mean than the boys. This is because the boys have more off their middle 50 percent closer to the mean than the girls. But if you look at the box and whisker diagram the range is bigger for the boys for Ks2 results and IQ. The inter-quartile range for the ks2 results is the same range but the boys is 11 to 15 and the girls are 10 to 14 this shows that the boys are consistently higher, this would also rule out extreme values.

Standard deviation shows the measure of spread, this shows the consistent they are in relation to the mean. The lower the standard deviation the more consistent the data is. The girls are more consistent than the boys because they have a smaller standard deviation. The standard deviation for the girls have a consistent deviation of 2.08 but the boys has a slightly higher 2.3. This shows that the boys and girls are all very close to the mean.

The mean IQ scores and ks2 results for the boys are slightly higher than the girls this shows that overall the boys have better grades than all the girls. The boys have a higher median IQ than the girls this shows that the boy's middle value is higher than the girls middle value. This tends to show that the boys IQ are higher but it does not represent the values either side of the median so it is not completely accurate. But the ks2 median results for both boys and girls are the same this shows that boys and girls have a similar level of intelligence. This means that my second hypothesis isn't proven.

The median and the inter-quartile range are more reliable than the mean and the range because the mean and the stand deviation can be changed a lot be an extreme result but the median and the inter-quartile range are not effected by extreme results. You could look for extreme results on a stem and leaf diagram by the base shape of distribution.

In my data the boys ks2 results and IQ graph shows strong positive correlation, my whole sample for ks2 results and IQ graph shows strong positive correlation, my data for the girls ks2 results and IQ graph shows strong positive correlation this proves my hypothesis which is that higher the IQ score higher the sats level because this shows that you have a high IQ you should also have a high ks2 results. I then used coefficient of rank correlation to further back up my hypothesis because this also shows how strong the correlation is, it did back up my hypothesis because the correlation was strong.

Conclusion

Due to my investigation I have learned that Ks2 results and IQ's are linked. My hypothesis is that the higher the IQ the higher the Ks2 results and now I can back this up because the three scatter diagrams and the spearman's rank correlation backed this up. All three scatter diagrams showed strong positive correlation and the spearman's rank of correlation further backed this up by showing how strong the correlation is. I also was investigating to determine if there is a significant difference between boy's ks2 results and IQ and girl's ks2 results and IQ. This was not clear cut because some of the results pointed to the boys being more clever but have less constancy overall. I found that there is not a significant difference between the boys and girls intelligence for example the box and whisker diagram showed the boys are less consistent over the full range but the boys are more consistent around the mean against the girls IQ and ks2 results.

There are limitations one was due to the fact that we took secondary data; this limits the accuracy this means we cannot prove my hypothesis because we don't know whether this data is true. We could improve this by getting our own data but there is a disadvantage of this it takes up time. Also it is a sample of the population so therefore it would not be completely accurate because we might have by chance randomly got all the clever boys and the not very clever girls. These problems could be resolved if there was more time.

We could improve this by taking more than 1 sample size of 100 this would make it more accurate. The ks2 results were combined this means that we could not study we couldn't look at whether maths, English or science correlated with a person's IQ.

My findings could not prove my hypothesis because the data is secondary also it is fictional this means that it could be biased. I could improve this by collecting my own data. I took a sample of the whole data so this sample could not represent all of the data fully. We only used data from one school this means it is a not very good spread of the all the people who has ks2 results and an IQ score.

There are practical consequences due to the scatter diagrams because you could use the line of best fit to predict what IQ they have if they have their Ks2 results. For examples if a girl moved a school the new school would want to know what ks2 results but if she only has her IQ, they could look on the scatter diagram for girls IQ score and ks2 and look on the line of best fit to predict her ks2 results.

I could further this investigation to make it more accurate by expanding the investigation, I could take a bigger sample size or used more than one sample, you could even use the whole school. You could investigate into gender comparisons over different ages to investigate back to back how the girls and boys intelligence differs.

BY

Adam Downes