This mini-lesson covers the Statistics strand of AQA GCSE Maths (8300): averages (mean, median, mode, range), frequency tables, grouped data & estimated mean, cumulative frequency, box plots, scatter graphs & correlation, and sampling.
These games test recall of facts, formulae and methods — not full multi-step working. Answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
Data: 4, 7, 7, 2, 5.
Mean = (4+7+7+2+5) ÷ 5 = 25 ÷ 5 = 5
Ordered: 2, 4, 5, 7, 7 → median = 5, mode = 7, range = 7 − 2 = 5
Order first for the median: the middle of the sorted list. For an even count, average the two middle values.
Multiply each value by its frequency (f × x), total those, then divide by the total frequency:
Value 1 (×3), value 2 (×5), value 3 (×2).
Σ(f×x) = 1×3 + 2×5 + 3×2 = 3 + 10 + 6 = 19
Σf = 3 + 5 + 2 = 10, so mean = 19 ÷ 10 = 1.9
Divide by Σf, not the number of rows: the denominator is the total frequency (10 here), not 3.
With grouped data you don't know exact values, so use the midpoint of each class as x, then find the mean as before:
Class 10 ≤ x < 20.
Midpoint = (10 + 20) ÷ 2 = 15
Why "estimated": you're assuming every value sits at the class midpoint, which isn't exactly true — so the mean is an estimate.
Cumulative frequency is a running total. From its graph you read the median and quartiles, which feed a box plot:
IQR vs range: the range uses the extremes; the IQR (UQ − LQ) ignores outliers and shows the spread of the middle 50%.
A scatter graph shows the relationship between two variables. The pattern describes the correlation:
Draw a line of best fit to estimate values in between.
Correlation ≠ cause: two things rising together doesn't prove one causes the other. And avoid predicting far outside the data (extrapolation) — it's unreliable.
A sample is a smaller group taken from a whole population. A good sample is random and representative so results generalise fairly.
In a sample of 50 people, 20 preferred tea. Estimate the number in a town of 5000.
Proportion = 20 ÷ 50 = 0.4, so 0.4 × 5000 = 2000 people
Bias: a sample taken only outside a coffee shop wouldn't represent the whole town — the method must be fair.
Tap a statistical term on the left, then its correct meaning on the right.
An average summarises the "typical" value; a measure of spread describes how varied the data is. Tap a term, then the box it belongs in.
Averages: mean = sum ÷ count; median = middle; mode = most common.
Spread: range = highest − lowest; IQR = UQ − LQ.
Frequency tables: mean = Σ(f×x) ÷ Σf.
Grouped data: use midpoints for an estimated mean.
Cumulative frequency & box plots: median & quartiles from a running total.
Scatter graphs: positive, negative or no correlation; line of best fit.
Sampling: fair, representative samples scale up to estimate a population.
You've covered every Statistics sub-topic in AQA 8300. Press Finish to see your score.
You've worked through Statistics for AQA GCSE Maths (8300). 🎉
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