Correlation definition
Correlation is a statistical idea that describes the relationship between two variables. A variable is something that can change, such as height, age, temperature, revision time or test score. If two variables are related in a pattern, we say there is correlation. Correlation is usually shown using a scatter graph, where each point represents a pair of values.
For example, a teacher might compare the number of hours students revise with their test marks. Each student would be represented by one point on a scatter graph. If students who revise more generally get higher marks, the points may rise from left to right. This is called positive correlation. It means that as one variable increases, the other variable also tends to increase.
Negative correlation happens when one variable tends to decrease as the other increases. For example, the number of hours spent watching television before an exam might have a negative correlation with exam score, if more screen time is linked with lower marks. On a scatter graph, negative correlation usually appears as points falling from left to right. No correlation means there is no clear pattern between the variables.
Correlation is used in statistics, data handling, scatter graphs, probability, science, geography, economics, psychology and real-world research. At GCSE level, students usually describe the type and strength of correlation from a scatter graph. They may also draw a line of best fit and use it to estimate values. At A-Level, correlation can connect to regression, hypothesis testing, bivariate data and numerical measures of association.
A line of best fit is a straight line drawn through the general pattern of points on a scatter graph. It does not have to pass through every point, but it should represent the overall trend. If the points are close to the line, the correlation is strong. If the points are spread out but still follow a pattern, the correlation is weak or moderate. If the points look random, there may be no correlation.
One very important warning is that correlation does not always mean causation. Causation means that one thing directly causes another. For example, ice cream sales and sunburn cases may both increase in hot weather. They are correlated, but buying ice cream does not cause sunburn. A third factor, temperature, affects both. This is a common idea in statistics and helps students avoid misleading conclusions.
Correlation can be described using words such as positive, negative, strong, weak, moderate or none. In more advanced maths, a correlation coefficient may be used to measure the strength and direction of the relationship. A value close to 1 suggests strong positive correlation, a value close to -1 suggests strong negative correlation, and a value near 0 suggests little or no linear correlation.
Understanding correlation is important because data is often used to make decisions. Businesses use correlation to study sales, schools use it to review performance, scientists use it to test relationships, and governments use it to understand trends. In maths exams, students must be careful to describe the relationship shown by the data, not make claims that are stronger than the evidence allows.
Related topics include scatter graphs, line of best fit, bivariate data, regression, outliers, averages, probability and data interpretation. Useful ideas include identifying trends, making estimates, spotting unusual points and explaining limitations. A clear definition of correlation helps students understand how two variables may be connected and how to interpret real data responsibly.