33 bits of data were presented with the case of the year 7 males.
Year 7-Female
29 needed for year 7 females.
Year 11-Male
18 pieces were selected in this case. With year 11 males we also come across our first piece or nominal data. Highlighted in red this piece of data is very unusual compared to the rest and to have an I.Q of 14 is near impossible, so you’ll see in occasions to come I will not use this bit of data, or will use it and say what comes of from using it.
Year 11-Female
19 pieces of data are presented in the case of the year 11 females.
Representation
Before I even look into comparisons and trying to prove or disprove my hypothesis I want o look at what the data is saying. Things such as seeing what percentage of the people in my collection got what Level, what levels do not appear at all.
This shows that the percentage of boys from year 7 in my sample received a level 4. This can help me conduct that level 4 seems to be the average result for KS2 results and is what people should be receiving; further pie charts will help me too.
This pie chart helps me too, to prove what I have said before. A 4 in KS2 seems to be the norm and is what we should look at to see a reasonable connection between an average I.Q and KS2 result of 4.
The same is said with both sexes from year 11, helping to give me an average to work with.
More pie charts and percentages help us to see norms to help us in justification.
The mode of the I.Q of all the sexes in all the years is 100. This points towards a score of 100 on an I.Q test is a good national child. Although we can not make this statement a 100% sure as we do not know when the population may have taken the test. i.e did the year 11’s do it when they were year 7’s or at the age they are at the time of the collection of data. This age difference will affect what there score symbolises to their actual I.Q.
The first representation of relationships and connections I can use is a scatter graph. With the use of correlation I can see whether there is a strong relationship between I.Q and KS2 result.
This graph shows a very strong relationship between I.Q and KS2 result, it seems to show an increase in one, leads to an increase in another, this is correlation. The correlation in this graph is very strong at 0.9- showing a very strong, positive correlation which helps me to prove my hypothesis.
Not such a strong correlation but still pretty strong is the relationship between I.Q and average KS2 results with year 7 females. The Correlation in this case being 0.85772- still a very strong positive correlation present.
The year 11 male’s relationship also shows the same thing apart from a big anomaly affecting the overall picture. With this anomaly in place it makes the correlation very bad, with it being -0.28458. Take away the anomaly though and you get a different picture. A correlation of 0.561255 is now present. Even though this shows a stronger relationship, compare it to the others and it looks bad. But at the core of this correlation it still shows a worthwhile connection.
The correlation here is 0.596643, still not as strong, but abundant enough to show us a relationship between I.Q and average KS2 result.
This joint graph of averages to I.Q also helps us to recognise a relationship; this one has a really strong positive correlation, with it being 0.911969.
The same can be said with the year 11’s although again the anomaly does affect it. The correlation in this situation being -0.04626, without the anomaly it is 0.608118, much stronger and showing a positive relationship.
The Correlation in this case, even including the anomaly is still pretty strong at 0.403289, without the anomaly it turns into 0.786475, much stronger.
This information presented in this table tells us a lot of information. First of all we can say articulate again which I have said before. Using the modes we can justify what I think to be a national average to which all aim for when taking either an I.Q (100) or KS2 (an overall average of 4.) Because of the smaller steps between I.Q deviation (i.e from 100-101 is quite a small change.) A change from 4-5 (as results are given in whole integer format) is quite big.
You can see just from the scatter graphs which have been produced there is definitely a relationship between I.Q and an average KS2 result. You can see that overall, the higher a persons I.Q the higher an average KS2 grade they will receive. This is shown through the correlation produced and the degree in which it is presented.
From here we can now go on and look at more things, such as who’s more intelligent? Males or Females? Is there any difference? And is there a difference between years? Were students born earlier on more intelligent?
From now on with my graphs I’m comparing the data with a KS2 result of 4 or above. This is because from this instance I’m now really focusing on intelligence and I think that Level 4 at KS2 is an average mark to get. Using this ‘average’ I can then relate my population’s I.Q and try to answer my queries.
With this radar graph we can see the relationships between the sexes, males combined from year 7+11 and the same with the females. It also shows them all combined. This graph is done on a cumulative scale and helps to show the increases. A steeper change in line meaning a bigger change in number. We can see over all the biggest change is through and about an I.Q of 100, this is what I thought to see/be the national average and the I.Q average to use in this investigation. This cumulative radar doesn’t help us with who may be more intelligent but others may.
This radar helps us with to see if there is a more intelligent sex as well as the pattern in which these increases take place. Here we can see that more males at the beginning have an I.Q of 90-99 and get an average KS2 result of 4 or more and the same kind of thing at the end of the scale. But in the middle you can see that using what we call my ‘average I.Q’ there are more females who have an I.Q of 100-109 and also get an average KS2 result of 4 or more. This can help me to put forward the point, that with this data we can say that females are more intelligent then males.
This graph also points towards the same kind of conclusion. I can see that in year 7 more females had an I.Q of 100-109 and received an average KS2 result of 4 or above. The modal class is represented in this middle percentage, in most cases being well over 50%.
The same can be said in this case, but with less definition. Females still reign over the place of an I.Q of 100-109 and an Average KS2 result or 4 or above, but in year 11 it can clearly be seen that males are close within the modal class and beat the females in numbers of those in I.Q 90-99 and 110-119.
Here when things are combined the same kind of pattern can be seen as in seen in the year 11 graph. Females coming out on top in periods but the males coming out in further sections of I.Q. This is where it can be hard to say if there is a clear cut difference between Male intelligence and Female intelligence.
With this type of graph it helps us to look at the matter of the intelligence, using what I list as my ‘average KS2’ score and what they should be getting. Using the graph we can see that overall the females finish on a higher number, interpreting this you could say that this may encourage the thought of females may be smarter. Using things like the median, quartiles etc can also help to reflect on what is being pictured. A higher median points towards the fact that there are more females getting the modal I.Q (what I think is the average measure) then males. More on the average means that overall you get more who are on the average whereas with the males you get a few who are above the average, more on the average and some below the average. This is proved through the calculations of the upper and lower quartile. Males have a bigger dispersion of intelligence, which means on the scheme of things if you take a class room of random males and females, the female population of that class is going to be more intelligent than the male.
In this case you can’t say the same kind of thing. The median in both cases is exactly the same, although again the males dominant in below and above the ‘average’ of mine. So in this case it can be seen that males are more intelligent.
With this information we can go back to what I said in the beginning. Again the females dominate the median, more females than males have what I call the average I.Q with ‘my’ average KS2 result of 4 or above. Not only can you see this with the table but with the sharper increase you can see for females on the graph, compared to the males at the sae time. But then the males have a sharper increase in the other two periods which also helps to prove the fact of dispersion. Where as the males have more dispersion with intelligence. There are more males than females above and below the modal class. With the females having a bigger inter-quartile range this proves the fact that there’s more space between the groups either side of the modal class, meaning there’s more females in the median group then the rest.
Summary
I’ve been able to prove the relationship between I.Q and what a person may get on average in their KS2 exams. It can be put forward that the higher a person’s I.Q is the higher their average KS2 result may be. But on top of that I have tried to see if there really is a definition between male intelligence and female intelligence. It is also in this case that I have also been able to come up with some justification to an answer to that. It can be seen (through what I have said before) that overall data suggests that there are more females more intelligent then males, but with males there is more dispersion of intelligence, and it is through this it can be read that there is therefore more individual males who are more intelligent the most females. Scenario- If you take a random class of females and males, with the same number of males as females. Using the data and interpretations it can be suggested that overall there would be more intelligent females than males, but there would be a few more males with above average intelligence than females.