Find the range, quartiles, interquartile range and percentiles, calculate the standard deviation, identify outliers, and draw and compare box plots of two distributions.

What this dot point is asking

Spread tells you how varied the data is, which an average alone cannot. CCEA expects you to find the range, the quartiles, the interquartile range and percentiles, to calculate the standard deviation, to identify outliers, and to draw and compare box plots. The standard deviation and the box-plot comparison are the higher-value skills here, and a full comparison of two data sets always pairs an average with a measure of spread.

The range, quartiles and IQR

The range (largest minus smallest) is the simplest measure of spread but is distorted by a single outlier.

The IQR is preferred over the range whenever outliers are present, because it describes the central bulk of the data rather than its extremes.

Identifying outliers

An outlier is a value far from the rest. A common rule treats a value as an outlier if it is more than $1.5 \times \text{IQR}$ below $Q_1$ or above $Q_3$. Outliers should be examined: they may be genuine extreme values or errors, and they strongly affect the mean and range but barely move the median and IQR.

The standard deviation

The standard deviation is the most informative measure of spread because it uses every value and its distance from the mean.

A smaller standard deviation means values cluster tightly around the mean; a larger one means they are more spread out. It is the measure of spread that pairs with the mean, just as the IQR pairs with the median.

Box plots and comparing distributions

A box plot (box-and-whisker diagram) is drawn on a scale and shows five values: the minimum, $Q_1$, the median, $Q_3$ and the maximum. The box spans the interquartile range, with a line at the median, and the whiskers reach the extremes.

To compare two distributions, compare an average and the spread, both in context. Compare medians to say which is higher on average, and compare interquartile ranges (or standard deviations) to say which is more consistent. A model answer is two sentences: "Group A has a higher median, so on average A is larger" and "Group A has a smaller IQR, so A is more consistent." Marks are lost for quoting figures without saying what they mean for the two groups.

Why this matters

Spread is half of every comparison and the natural partner to averages in the analysis stage of the enquiry cycle. The quartiles link straight back to cumulative frequency curves, the standard deviation underpins standardised scores and the normal distribution at Higher tier, and box plots are a standard way to summarise and compare data in real reports. Choosing the right pairing (mean with standard deviation, median with IQR) is a judgement CCEA rewards.