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AQA GCSE Maths (8300) · Statistics
Mini-Lesson

Statistics

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.

mean = (sum of values) ÷ (number of values)median = middle · mode = most common · range = highest − lowest

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.

Averages & range

Mean, median, mode & range

  • Mean: add all values, divide by how many there are.
  • Median: put in order, take the middle value.
  • Mode: the most common value.
  • Range: highest − lowest (a measure of spread, not an average).
Worked example

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.

Calculate

Your turn — the mean

1Work out the mean of 3, 8, 10, 6, 3.
Hint: sum = 3+8+10+6+3 = 30, then ÷ 5.
Calculate

Your turn — the range

2Find the range of 12, 5, 18, 9, 7.
Hint: range = highest − lowest = 18 − 5.
Frequency tables

Mean from a frequency table

Multiply each value by its frequency (f × x), total those, then divide by the total frequency:

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

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.

Calculate

Your turn — total from a table

3Goals per match: 0 goals (×4 matches), 1 goal (×3), 2 goals (×3). Work out the total number of goals scored.
Hint: Σ(f×x) = 0×4 + 1×3 + 2×3.
Grouped data · estimated mean

Estimated mean of grouped data

With grouped data you don't know exact values, so use the midpoint of each class as x, then find the mean as before:

estimated mean = Σ(f × midpoint) ÷ Σfmidpoint = (lower + upper) ÷ 2
Worked example — a midpoint

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.

Calculate

Your turn — class midpoint

4Work out the midpoint of the class 20 ≤ x < 30.
Hint: midpoint = (20 + 30) ÷ 2.
Cumulative frequency & box plots

Cumulative frequency & box plots

Cumulative frequency is a running total. From its graph you read the median and quartiles, which feed a box plot:

IQR = upper quartile − lower quartilethe interquartile range measures the spread of the middle half
min LQ median UQ max
A box plot shows five numbers: min, lower quartile, median, upper quartile, max.

IQR vs range: the range uses the extremes; the IQR (UQ − LQ) ignores outliers and shows the spread of the middle 50%.

Calculate

Your turn — interquartile range

5A data set has lower quartile 14 and upper quartile 27. Work out the interquartile range.
Hint: IQR = upper quartile − lower quartile = 27 − 14.
Scatter graphs & correlation

Scatter graphs & correlation

A scatter graph shows the relationship between two variables. The pattern describes the correlation:

  • Positive: as one goes up, the other goes up.
  • Negative: as one goes up, the other goes down.
  • No correlation: no clear pattern.

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.

Quick check

Name the correlation

?As the temperature rises, hot-chocolate sales fall. What type of correlation is this?
Sampling

Sampling

A sample is a smaller group taken from a whole population. A good sample is random and representative so results generalise fairly.

estimate = (sample result) scaled to the populationbigger, fairer samples give more reliable estimates
Worked example

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.

Calculate

Your turn — estimate from a sample

6In a sample of 40 fish, 6 were tagged. If the proportion is the same in the whole lake of 800 fish, estimate how many are tagged.
Hint: proportion = 6 ÷ 40 = 0.15, then × 800.
Quick check

Find the median

?What is the median of 8, 3, 9, 3, 6?
Match game

Match: term ⇄ meaning

Tap a statistical term on the left, then its correct meaning on the right.

Sort it

Average or measure of spread?

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.

📍 Average

↔️ Spread

Recap

The whole Statistics strand

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.

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Mini-lesson complete!

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