Describing a population using statistics

Most WJEC Unit 2 papers include a statistics question worth 4–6 marks where the candidate must describe a data set using averages and a measure of spread.

Three averages

Average	Definition	When to use
Mean	sum ÷ count	Quantitative data, no extreme outliers
Median	middle value when ordered	Skewed data or with outliers
Mode	most frequent value	Categorical data; only sensible for repeated values

For an even number of values, the median is the mean of the two middle values.

Measures of spread

• Range = highest − lowest. Affected by outliers.
• Interquartile range (IQR) = upper quartile − lower quartile. WJEC Higher only. Robust against outliers.

Frequency tables

For a frequency table with values x and frequencies f:

• mean = (Σ f × x) ÷ Σ f
• median position = (Σ f + 1) ÷ 2
• mode = the x with the largest f

For grouped data you cannot find an exact mean — use mid-interval values × frequency to estimate it. Always say "estimated mean" in the answer and write "(midpoint)" beside the multiplication line.

Comparing two data sets

WJEC always wants TWO comparisons:

1. An average (with numerical values).
2. A measure of spread (with numerical values).

Example wording: "The mean for class A (52.4) is higher than for class B (48.1) so class A scored higher on average. The range for class A (24) is smaller than for class B (37) so class A's scores were more consistent."

WJEC exam tip

When a question asks to "compare" two distributions, always quote two numerical values per comparison and use comparative language ("higher", "more spread"). Saying "class A is bigger" loses the A1 — it must be specific.