IQ Between Students in MayfieldHigh School

Scatter Diagrams:

Scatter diagrams are used to study possible relationships between two variables. Although these diagrams cannot prove that one variable causes the other, they do indicate the existence of a relationship, as well as the strength of that relationship. The purpose of the scatter diagram is to display what happens to one variables when another variable is changed. The diagram is used to test a theory that the two variables are related. The type of relationship that exits is indicated by the slope of the diagram.

* The Relationship Between IQ and KS2 Results - Scatter Diagram - The scatter diagram is used to see if there is a connection between the two sets of data.

Box and Whisker Diagram:

A box and whisker diagram illustrates the spread of a set of data. It also displays the upper quartile, lower quartile and interquartile range of the data set. The median is the middle value - half of the data set is below and half is above. The upper quartile is the value which 3/4 of the data set is below and 1/4 is above. It can be considered as the median of the upper half of the values in the set. The lower quartile is the value which 1/4 of the data set are below and 3/4 are above. It can be considered as the median of the lower half of all the values in the set. The interquartile range is the difference in value between the upper quartile and the lower quartile values.

* The Relationship Between Male and Female Student's IQ - Box and Whisker Diagram, Cumulative Frequency Diagram

* The IQ relationship Between different year groups - Box and Whisker Diagram, Cumulative Frequency Diagram

The first investigation I did was compared the general case for IQ against Key Stage 2 Results. I did this by plotting a scatter diagram. KS2 Results will be plotted on the X axis and the IQ on the Y axis. Then I would plot each students KS2 results and IQ on the graph. After all students have been plotted, I would then find the line of best fit and see if there is a correlation between KS2 Results and IQ. I worked out the line of best fit by finding the mean of all the KS2 results and IQ then plot it on to the graph. By extending the 2 points they would soon meet and if we draw another line through that, it would give us the line of best fit. After finding the line of best fit, I realized there was a correlation; however, it is very weak. But it was still possible to see a positive correlation through the scatter diagram.

Next, I investigated the IQ of students in more detail by comparing the IQ of male and female students. I plotted the results using a box and whisker diagram. In order to draw a box and whisker diagram, we would need the lower quartile, upper quartile and the median. I used the cumulative frequency diagram to find the lower quartile the upper quartile. Before drawing the cumulative frequency diagram, we need to work out the cumulative frequencies. This is done by adding the frequencies in turn. The cumulative frequency would then be plotted on the Y axis while IQ is plotted on the X. The Upper and lower quartile is worked out by multiplying the highest data by 0.75 for the upper quartile and 0.25 for the lower quartile. The lower quartile, upper quartile, median, largest data value and smallest data value would be plotted on a different graph like this:

The diagram clearly shows us that female students tend to have a higher IQ than male students and my prediction was wrong.

Lastly, I compared the IQ between each year group again, using the box and whisker diagram. The graph showed that on average, year 8 has the highest IQ and year 10 has the lowest.

My calculations have helped me to state that on average, the higher the IQ, the higher the key stage 2 results. Also female students tend to have a higher IQ than male students as we can see clearly from the box and whisker diagram. The IQ relationship between different year groups did not show a correlation or a pattern. However, it showed us that year 8 has the highest IQ while year 10 has the lowest. This has proven my original statements to be correct other than the IQ relationships between different year groups. I predicted that the higher grades will have higher IQs which are not correct. I am happy that my conclusions are reliable because my data did not show any anomalous results meaning I did not make any errors during the process of calculations.

Francesco Chan 10J