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Mayfield School Statistics - IQ Correlation

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In this investigation I need to select data from which I can make sensible conclusions that support my hypothesis.

I have selected I.Q results and Sat Results from girls in year 10 to see if one variable depends on the other.

Hypothesis: The higher the I.Q the higher the Sats Results.


Firstly, I am going to draw a scatter graph to see if there is a relationship between the independent and dependant variables. The independent variable is going to be plotted horizontally and dependant variable vertically. This is because the dependant variable depends on the independent variable.

In this investigation I choose both variables, nevertheless one variable always depends on the other. Therefore the independent variable is the I.Q and the dependant is the Sats Results. So in my theory, your Sats Result should always depends on your I.Q.  

Once I had plotted the graph (see appendix 1) I wanted to find the regression line and correlation coefficient.

...read more.


r= 0.5648 you would say that it has a weaker positive linier correlation. Basically a correlation coefficient tells how good a correlation you have in your graph.

Although the correlation coefficient can be found without plotting a scatter graph it is always more useful to, as it gives you a picture of the correlation and also helps distinguish any outliners.

I have done a correlation coefficient for my data. (See appendix 3)

As can be seen the correlation coefficient is r = 0.911465 which means that there is a very strong positive correlation between I.Q and Sats Results, telling me that

I.Q does affect Sats Results because of this strong correlation.

Regression Line?

To obtain the regression line there are steps that have to be followed:

  1. Gradient meaning that the straight-line law y=a+bx has to be used. Since the line is a straight line, we use y=a+bx.

b = gradient found using:

In this case the gradient is how much the sat total increases for every 1 I.Q point increase.

...read more.


The one way in which I could extend my investigation is by plotting the average number of hours TV watched per week against the I.Q and Sats Results to see weather the amount of TV watched affects I.Q and Sats Results.

 In order to do this I would have to consolidate I.Q and Sats results in to one value.

The way in which this is done is by using this formula:

                       = 1 average score  

> 1 means better than expected results

< 1 means poorer than expected results

To see how the above equation was obtained see appendix 4.


This number would be plotted against the average number of hours TV watched per week.

This I would have done but did not for 2 reasons:

  1. All the values are only 20% apart
  2. From looking at the raw data I saw no correlation as was very random (see appendix 3)

A further extension I could do is plot the consolidated values against other factors that could effect the I.Q and Sats Results such as; How much homework they do? Do they have brothers or sisters? What kind of foods they eat?

...read more.

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