Calculate and interpret standardised scores using the mean and standard deviation to compare values across different distributions, and describe the skewness of a distribution.

What this dot point is asking

Comparing a value from one data set with a value from another with a different mean and spread is unfair unless you put them on the same footing. CCEA expects you to calculate a standardised score, which says how many standard deviations a value is above or below its mean, and to use it to compare across distributions. You also need to describe the skewness of a distribution. These are Higher-tier ideas that build directly on the mean and standard deviation.

The standardised score

A standardised score (sometimes called a z-score) rescales a value relative to its own distribution.

The point is fair comparison. A raw mark of 75 in one test and 66 in another cannot be compared directly if the tests had different means and spreads, but their standardised scores can, because both are measured in standard deviations from their own means.

Comparing across distributions

A larger standardised score means a more exceptional result relative to the group, which is exactly how the comparison marks are earned.

Describing skewness

Skewness describes whether a distribution is symmetrical or has a longer tail on one side.

You can judge skew from a box plot too: if the right whisker and the right half of the box are longer, the data is positively skewed; if the left side is longer, it is negatively skewed.

Why this matters

Standardised scores are how examiners, psychologists and sports scientists compare results measured on different scales, and they lead directly into the normal distribution at Higher tier, where standardised scores of $\pm 1, \pm 2, \pm 3$ correspond to the 68 to 95 to 99.7 percentages. Describing skewness connects averages, spread and shape, and explains why the mean and median differ for real data such as incomes. Both skills reward a clear interpretation, not just a number.