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# AQA A-level Maths Interpreting diagrams 1. Correlation
2. Interpolation
3. Extrapolation

Scatter graphs can be used to investigate the correlation between the variables they represent. The variables can have a positive, negative or no correlation, depending on the steepness of the pattern the scatter points follow. The two variables that are positively correlated increase together and two variables which are negatively correlated decrease together. Although two variables can be correlated, it does not necessarily mean that the one variable causes the other, as there may be a third one that affects both. Thus, it can be said that correlation does not imply causation. The line of best fit of a scatter plot can be used for interpolation. Interpolation is the process used to estimate the value of the dependent variable from the independent one without a scatter point for that value. For interpolation to work, the value must lie within the range of the values of the graph. Extrapolation is the process used to estimate the value of the dependent variable from the independent one without a scatter point for that value for values which are outside the recorded range. Since the values are not within the range, estimates made by extrapolation are less accurate than those made by interpolation. # 1

Describe what you would expect the relationship between the number of ice creams sold and the number of flipflops sold to be. # 2

What values is interpolation carried out for? # 3

The heights and masses of a group of students are recorded. The shortest student has height 156 cm and the tallest student has height 172 cm. Explain whether making a prediction for the mass of a student of height 180 cm using this data is interpolation. # 4

The number of books read in a year by a set of students is recorded alongside their percentage grade in English Literature and the two variables are found to be positively correlated. The number of books read by the students ranged from 3 to 55. Explain whether an estimation for the English Literature grade of a student who read 38 books or one who read 0 books would be more accurate. # 5

Match the given scatter plots to the following pairs of variables: (1) number of hours spent studying in a week and the percentage grade received by the student, (2) number of weeks since a student studies a topic and their memory of that topic, (3) the number of guitars sold in a year and the number of coats sold in a year. End of page