GCSE

Statistics & Data

Reading charts, comparing distributions, and understanding what the numbers actually mean in context.

What Your Child Is Learning

GCSE statistics is about reading, interpreting, and comparing data. Your child needs to work with a range of chart types and draw meaningful conclusions from them:

Bar charts & pie charts — comparing categories
Scatter graphs — showing the relationship between two variables
HigherHistograms — displaying grouped continuous data using frequency density (not just bar height)
HigherCumulative frequency diagrams — finding medians and quartiles from grouped data
HigherBox plots — summarising a distribution with five key values (minimum, lower quartile, median, upper quartile, maximum)

The emphasis is on interpretation — not just reading the number, but explaining what it means in the real-world context of the question.

How Schools Teach It Now

Students are taught to compare distributions using two measures:

An average (usually the median) — tells you a typical value.
A measure of spread (usually the range or interquartile range) — tells you how consistent the data is.

For scatter graphs, they learn to describe correlation:

Positive correlation — as one variable increases, so does the other.
Negative correlation — as one increases, the other decreases.
No correlation — no clear pattern.

HigherKey vocabulary: the interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). It measures the spread of the middle 50% of the data, and is more reliable than the range because it ignores outliers.

$$\text{IQR} = Q_3 - Q_1$$

Common Mistakes to Watch For

HigherReading the wrong axis: on cumulative frequency diagrams, students read across from the frequency axis when they should read up from it (or vice versa). Always check which axis the question is asking about.
HigherConfusing frequency with cumulative frequency: the cumulative frequency at a value is the running total up to that point, not the count in that single group. Plotting raw frequencies on a cumulative frequency diagram produces a completely wrong curve.
Describing correlation casually: "the more hours you revise, the more marks you get" states it as a certainty. Describe correlation in context, e.g. "as hours revised increase, marks tend to increase".
Not answering in context: "the median is higher" is incomplete. "The median score for Class A is higher, which suggests students in Class A typically performed better on the test" is usually what examiners want.

Try It Together

HigherWorked Example — Reading a Box Plot

Given: A box plot shows these values:

Minimum = 15
Lower quartile (Q1) = 30
Median = 45
Upper quartile (Q3) = 60
Maximum = 80

Question: What is the interquartile range, and what does it tell us?

$$\text{IQR} = Q_3 - Q_1 = 60 - 30 = 30$$

Interpretation: The middle 50% of the data falls between 30 and 60. An IQR of 30 means there is a fairly wide spread in the central half of the data.

Bonus question: What fraction of the data lies between 30 and 60? Answer: about half (roughly 50%), by definition of quartiles.

Let Them Practise

Free game on MaffsGames:

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