This mini-lesson covers the core Handling Data content of CCEA GCSE Mathematics: the averages (mean, median, mode) and range, frequency tables & grouped data, cumulative frequency, scatter graphs & correlation, and probability — the scale, tree diagrams and relative frequency.
Honest heads-up: these quick questions test your recall of facts, formulae and methods — they can't mark full written working. In the real exam you must always show each step.
Work through each screen, answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
Four measures you must know cold:
Data: 4, 7, 8, 5, 6.
Mean = (4 + 7 + 8 + 5 + 6) ÷ 5 = 30 ÷ 5 = 6
Ordered: 4, 5, 6, 7, 8 → median = 6 (middle value)
Range is a spread, not an average: it measures how spread out the data is (biggest − smallest), while mean, median and mode measure the "middle".
Median: put the values in order, then take the middle one. With an even number of values, take the mean of the middle two.
Data: 3, 7, 2, 9, 5.
Order: 2, 3, 5, 7, 9 → median = 5 (the 3rd of 5 values)
Range = 9 − 2 = 7
Order first, always: the biggest mistake is reading the median off the unordered list. Sort the data before you pick the middle.
When data is in a frequency table, multiply each value (x) by its frequency (f), total the products, then divide by the total frequency:
Value 1 (×4), value 2 (×5), value 3 (×1).
Σ(f × x) = 1×4 + 2×5 + 3×1 = 4 + 10 + 3 = 17
Σf = 4 + 5 + 1 = 10 → mean = 17 ÷ 10 = 1.7
Grouped data: when values come in class intervals, use the midpoint of each class as x. The result is an estimated mean.
Cumulative frequency is a running total of the frequencies — a count of "how many so far". Plot it against the upper class boundary to get an S-shaped curve.
Frequencies: 3, then 5, then 4, then 2.
Cumulative: 3 → 3+5 = 8 → 8+4 = 12 → 12+2 = 14
Reading the curve: the median is found at ½ of the total on the cumulative axis; the quartiles at ¼ and ¾. The interquartile range = upper quartile − lower quartile.
A scatter graph shows whether two variables are linked. The pattern of points tells you the correlation:
Correlation is not cause: a link between two variables does not prove one causes the other. Ice-cream sales and sunburn both rise in summer, but neither causes the other.
Probability runs from 0 (impossible) to 1 (certain). For equally likely outcomes:
Probabilities must total 1: if P(rain) = 0.3, then P(no rain) = 1 − 0.3 = 0.7. A probability can never be more than 1 or less than 0.
A tree diagram shows combined events. The rule:
Branch check: at every split, the branch probabilities add to 1 (here 0.4 + 0.6 = 1). If they don't, you've made a slip.
When outcomes may not be equally likely, estimate probability from experiment using relative frequency:
A coin is flipped 50 times and lands heads 20 times.
Relative frequency of heads = 20 ÷ 50 = 0.4
More trials = more reliable: a few flips can be misleading, but over thousands of trials the relative frequency settles near the true probability.
Tap a statistic on the left, then its matching definition on the right.
A probability must be between 0 and 1. Tap a value, then the box it belongs in.
Averages: mean = total ÷ count; median = middle (order first); mode = most common; range = biggest − smallest.
Frequency tables: mean = Σ(f×x) ÷ Σf; use midpoints for grouped data (estimated mean).
Cumulative frequency: a running total; read median and quartiles from the curve.
Scatter & correlation: positive, negative or none; a line of best fit shows the trend; correlation ≠ cause.
Probability: scale 0 to 1; P = favourable ÷ total; opposite events add to 1.
Tree diagrams: multiply along branches, add between paths.
Relative frequency: successes ÷ trials; more trials give a better estimate.
You've covered the core Handling Data content of CCEA GCSE Mathematics. Press Finish to see your score.
You've worked through Handling Data for CCEA GCSE Mathematics. 🎉
Your stars: 0 / 0
Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.