Analysing and interpreting data, calculating the mean, median, mode and range, and drawing conclusions to evaluate performance.

What this dot point is asking

AQA wants you to analyse and interpret data, calculate the mean, median, mode and range, read information from graphs and tables, and draw valid conclusions to evaluate performance.

Calculating averages and range

For the data set 4, 6, 6, 8, 11: the mean is $\frac{4 + 6 + 6 + 8 + 11}{5} = 7$, the median is 6 (the middle value), the mode is 6 (most common), and the range is $11 - 4 = 7$.

Each average tells you something different, and AQA expects you to know when each is useful. The mean uses every value, so it is the most representative average, but it is distorted by a single very high or very low value (an outlier), for example one injured player with a very poor score. The median ignores the size of the extreme values, so it is more reliable when there is an outlier. The mode is the only average that works for non-numerical categories, such as the most popular sport in a survey. The range measures the spread or consistency of the data: a small range means the values are close together (a consistent performer or squad), while a large range means they are widely spread (inconsistent). When there is an even number of values, the median is the mean of the two middle numbers; for example the median of $4, 6, 8, 10$ is $\frac{6 + 8}{2} = 7$.

Reading graphs and trends

Drawing conclusions

A good conclusion uses the actual figures, links back to the original question, and is justified by the data rather than by opinion.

A strong answer also distinguishes describing the data from explaining it. Describing means stating what the data shows, for example "the resting heart rate fell by 8 beats per minute". Explaining means giving the reason, for example "because the cardiovascular system has adapted to training with cardiac hypertrophy and a larger stroke volume". The highest marks come from doing both, then drawing the conclusion that links back to the question. It is also good practice to recognise the limits of the data: a single test, a small sample, or one anomalous result may not be enough to be sure, so a careful conclusion notes whether more data would strengthen the judgement. Treating one improved score as proof that a whole programme works is a classic over-claim that examiners penalise.

Worked example