I would like to know whether there is a link between ability in Maths and in Science in the Year 7, 8 and 9 students at Mayfield High School.

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Introduction

I would like to know whether there is a link between ability in Maths and in Science in the Year 7, 8 and 9 students at Mayfield High School.  My initial thoughts are that there is a link between the two because Maths and Science share some of the same attributes – they both involve formulae, they both require logical ability, and they both use numbers.  Furthermore, I think that someone with an interest in Maths will also have an interest in Science, and so will probably work hard at both.

Data Collection

To investigate this link, I will use the Key Stage 2 results from the Mayfield High School database.  There are 813 Year 7, 8 and 9 students listed in the database, so to save time I will base my investigation on a sample of 30 of these students.

Bias is anything that occurs when taking a sample that might prevent the sample from being a true representation of its parent population.  To avoid bias, I will ensure that my selection of the sample is completely random.  To ensure a random selection, I will use a random number generator on my calculator.  In the database, the students are numbered from 1 to 813.  As the random numbers appear on my calculator, I will record the associated data in two or three tables, once for all 30 students, one just for males and one just for females.  I have decided to do this as I suspect that any link between ability in Maths and in Science may also in turn be linked to gender.

Finally, before I collect my data, I will express one concern I have regarding the Mayfield High School database.  Studying the database, I notice that one or two IQ values have been entered as low as 11 and 14.  These are quite clearly inaccurate.  I therefore fear some of the other data may have been inaccurately entered into the database.  However, it is impossible to tell in the case of most of the other columns and therefore, I must simply resolve to just look out for any abnormalities in my calculations or diagrams that may be accounted to inaccurate data in the database.

After generating 30 random numbers, I now have the set of data shown in Appendix A at the rear of this project to base my investigation on.


Analysis

To start with, I will analyse the first table of data, where the data is not gender-specific.  Before I show you my analysis, I will just mention that I have left out the zero values as I feel that these may be further evidence of inaccuracies within the database; any student granted a 0 in Maths and a 0 in Science would have been absent on the day and therefore these values will only distort my analysis.

So, to start, I will initially calculate the measures of spread and location listed in the table below:

[Table 1: Basic Measures of Spread and Location]

Studying the table, a first point to note is that if the mean and median are not exactly the same, they are indeed very close.  This indicates that there is little, if any, skewness in the data.

When the distribution of data is not symmetrical, it is known as a skew distribution.  If the tail of the distribution extends in the direction of the positive axis, then the distribution is positively skewed and in the other direction negatively skewed.  I will now calculate the coefficient of skewness associated with each of these sets of results to confirm that there is indeed little skewness in the data.  Below is a table illustrating these values:

[Table 2: Coefficients Of Skewness]

As previously suggested, this table does indeed confirm that in both cases there is little, if any, skewness in the data.  I am pleased with this result because it therefore not only allows me to conclude that in both Science and Maths, the students on average scored a level 4 in their Key Stage 2 exams, but also suggest that since these scores are the same, there is a link between ability in Maths and ability in Science.

Moving away from calculations and onto diagrammatic representation, I will now extend my analysis to the use of scatter diagrams.  With the x-axis as Maths and the y-axis as Science, I produced the scatter diagram inserted over the page.


Studying the scatter diagram, it is clear that there is a link between the Key Stage 2 results for Maths and Science; students who scored high in Maths were more than likely to have scored high in Science.  Therefore, since positive correlation is clearly indicated by the scatter diagram, I can conclude that there is a link between ability in Maths and ability in Science.

For all intents and purposes, having now established, on the basis of my sample of 30 students, that there is a link between ability in Maths and ability in Science, I have now fulfilled my aim and could conclude my project.  However, having already separated my sample data into a male / female divide, I shall see whether the link between ability in Maths and ability in Science is in turn linked to gender.

To extend my analysis in such a manner, I will now repeat the previous calculations for the second and third tables in appendix A at the rear of this project.  Below are two tables to show the result of my calculations:

[Tables 3 and 4: Male / Female Measures Of Spread And Skewness]

Studying these values together with the combined scatter diagram inserted over the page, I can reach a conclusion.  With the coefficients of skewness approximately the same as before, I can once again conclude that on average, regardless of their sex, the students scored a level 4 in both their Maths and their Science Key Stage 2 exams, and that there is a link between ability in Maths and ability in Science.

However, if we study the scatter diagram further, we can see that this is not all it suggests!  While both male and female students who scored high in Maths were more than likely to have scored high in Science, two further statements can also be made:

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  • On average, both the male and female students showed greater ability in Science than in Maths.
  • On average, the link between ability in Science and in Maths is greater for male students that for female students.

Since both these statements interest me and require further analysis to quantify, I shall now investigate whether there are any mathematical techniques that could be used to do so.




 I see that you can calculate a measure of the correlation in the scatter diagram.  This measure is called the product-moment correlation coefficient and is considered powerful as it ...

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