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CCEA GCSE Maths · Handling Data
Mini-Lesson

Handling Data

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.

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Data becomes information: averages, spread, patterns and chance.

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.

Data · Averages

Mean, median, mode & range

Four measures you must know cold:

mean = total ÷ how manymedian = middle value (order first) · mode = most common · range = biggest − smallest
Worked example

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".

Calculate

Your turn — the mean

1Work out the mean of 4, 7, 8, 5, 6.
Hint: add them (= 30), then divide by 5.
Data · Median, mode & range

Median, mode & range in detail

Median: put the values in order, then take the middle one. With an even number of values, take the mean of the middle two.

Worked example

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.

Calculate

Your turn — the median

2Find the median of 12, 5, 8, 20, 3.
Hint: order them (3, 5, 8, 12, 20), then take the middle value.
Quick check

Find the mode

?What is the mode of 2, 4, 4, 5, 7, 4?
Calculate

Your turn — the range

3Work out the range of 3, 5, 8, 12, 20.
Hint: range = biggest − smallest = 20 − 3.
Data · Frequency tables

Mean from a frequency table

When data is in a frequency table, multiply each value (x) by its frequency (f), total the products, then divide by the total frequency:

mean = Σ(f × x) ÷ ΣfΣ means "the sum of" — add up the column
Worked example

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.

Calculate

Your turn — mean from a table

4A table shows: value 1 occurs 4 times, value 2 occurs 5 times, value 3 occurs 1 time. Work out the mean.
Hint: Σ(f×x) = 4 + 10 + 3 = 17, and Σf = 10, so 17 ÷ 10.
Data · Cumulative frequency

Cumulative frequency

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.

Worked example — the running total

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.

Calculate

Your turn — cumulative frequency

5The frequencies are 3, 5, 4 and 2. What is the total cumulative frequency (the final running total)?
Hint: it's the total of all the frequencies: 3 + 5 + 4 + 2.
Data · Scatter & correlation

Scatter graphs & correlation

A scatter graph shows whether two variables are linked. The pattern of points tells you the correlation:

positive · negative · nonepositive = both rise · negative = one rises as the other falls · none = no pattern
positive correlation
Points rising left-to-right show positive correlation; a line of best fit summarises the trend.

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.

Quick check

Name the correlation

?As the temperature rises, the amount of hot soup sold falls. What correlation is this?
Data · Probability

The probability scale

Probability runs from 0 (impossible) to 1 (certain). For equally likely outcomes:

P(event) = favourable ÷ totalall the probabilities of an event and its opposite add to 1
0 ½ 1 impossible even chance certain
Rolling an even number on a fair die: 3 favourable ÷ 6 total = ½.

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.

Calculate

Your turn — a single die

6A fair six-sided die is rolled. Work out the probability of rolling an even number. Give your answer as a decimal.
Hint: even numbers are 2, 4, 6 — that's 3 out of 6, so 3 ÷ 6.
Data · Tree diagrams

Tree diagrams

A tree diagram shows combined events. The rule:

multiply along branches · add between pathseach set of branches from a point must add to 1
0.4 R 0.6 B 0.4 R 0.6 B 0.4 R 0.6 B RR = 0.16
P(red then red) = 0.4 × 0.4 = 0.16 — multiply along the branches.

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.

Quick check

Along the branches

?A spinner lands on red with probability 0.4. It is spun twice. What is P(red then red)?
Data · Relative frequency

Relative frequency

When outcomes may not be equally likely, estimate probability from experiment using relative frequency:

relative frequency = successes ÷ trialsthe more trials, the closer it gets to the true probability
Worked example

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.

Calculate

Your turn — relative frequency

7A drawing pin is dropped 200 times and lands "point up" 90 times. Work out the relative frequency of "point up". Give your answer as a decimal.
Hint: 90 ÷ 200.
Match game

Statistic ⇄ meaning

Tap a statistic on the left, then its matching definition on the right.

Sort it

Valid or impossible probability?

A probability must be between 0 and 1. Tap a value, then the box it belongs in.

✅ Valid (0 to 1)

🚫 Impossible

Recap

The whole of Handling Data

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.

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