Bivariate Data

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Bivariate Data

        I am going to carry out an investigation into a set of bivariate data. The data I will investigate are a previous year groups KS3 and GCSE point score averages. I will see, whether or not there is a correlation between the KS3 and GCSE result scores.

        By finding a correlation or not, I will be able to determine if the scores obtained at KS3 will allow teachers to predict the student’s score at GCSE. If there is a strong correlation, this will be very useful for teachers and students to give them an idea on what they can be expected to score. Grade Predictions would be easier and probably more accurate.

        For example, if there is a correlation, a student could predict their GCSE score by using the KS3 results they obtained, and with this would provide a target score to reach or beat. This will also be useful for the teacher where they will be able to overview any additional help or teaching that a student may or may not need.


The Population (presented in table 1) shows last year’s groups, KS3 and GCSE point score averages. There are a total of 90 pieces of data. This is a fairly small population but it was the only set easily available. From the 90 I will randomly sample 50 pieces to investigate.

The way I randomly sampled the population, was to number each set one to ninety (1-90), while also numbering ninety pieces of paper. I placed those pieces of data into a hat, mixed them around and then picked out fifty from it. To make sure I didn’t accidentally “see” a numbered piece of paper, I folded the paper twice and blinded folded myself so I would be oblivious as to what I chose. The fifty I have chosen have been coloured in red and have also been placed into a table together (table 2).

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 I have presented the sample on a Scatter diagram (graph 1). The KS3 data has been plotted on the x-axis and the GCSE results on the y-axis. This is because in general, y is dependent on x, and so in this case the scores of the GCSE will depend on the performance achieved in KS3. That is why they have been plotted as shown. For the x-axis, I have placed a break from 0 to 3, because the smallest piece of data I have for KS3 is 3.7 and it is very unlikely that any student will get below 3 ...

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