Measures and calculations

The median is a two-step calculation and candidates skip step one. Rank the scores first — that alone is creditworthy working even if the final value is wrong. Then, with an even number, add the middle two and divide by 2. The errors: adding the middle two but not halving, dropping a data point so an even set looks odd, and picking one middle value instead of averaging.

This is the definition trap. A ratio or fraction is not finished until it is in simplest form, because the scheme states that value and nothing else scores. An unsimplified ratio like 11:11 must reduce to 1:1; where the answer is one half, two quarters scores zero. Order matters: for the ratio of A to B, writing B to A scores zero. Cancel by the highest common factor.

Calculations are usually a strength, but two stay weak. Percentage decrease: divide the change by the original value, then multiply by 100, and label it a decrease — dividing by the new value is the classic slip. Definitive answers: where the scheme states one figure, close does not score. A correct total still earns a mark even when the percentage is wrong, so show it.

The mean is the total of the scores divided by how many there are, and the reported failure is finding the total and then stopping. Add every score, then divide by the count; the total alone is not the mean. Count the scores before dividing, and obey any "to 2 decimal places" instruction — decimal places are not significant figures.

The range is the highest score minus the lowest — a single number. Two errors recur: quoting the highest score itself instead of the subtraction, and writing the extremes as a pair such as "17 to 41" rather than doing the sum. Always subtract: highest minus lowest. It tells you how spread out the scores are, not where their centre lies, from those two values alone.

The mode is the most common score in the data — the value itself, not how many times it occurs. If 6 appears three times, more than any other value, the mode is 6, not 3. Two more slips: reading off the middle score (the median) or the largest instead of the most frequent, and assuming there is exactly one mode when a set can be bimodal or have none.

The range is often misread as a statement about the typical participant — "most people scored around the middle". It does not: it uses only the highest and lowest score. So one unusual participant can inflate the range while the rest stay clustered, and two groups can share a range yet be distributed completely differently. With one extreme score, the median beats the mean.

Because 11.2.2 is the calculations statement, candidates assume the normal distribution sub-point must be a calculation too. It is not: 11.2.2h asks you to know the characteristics, answered in words — symmetrical, bell-shaped, mean, median and mode together at the centre, most scores near the middle, few extreme scores. A skewed, one-sided distribution is not normal.