Mean, median, mode & range

Four ways to summarise a list of numbers. Learn exactly what each one does:

Common slip: you must sort the list before taking the median. For an even number of values the median is the mean of the middle two.

Your turn — the mean

Your turn — the median

Median of an even list

Your turn — the range

Mean from a frequency table

When data is grouped in a frequency table, add an f × x column, total it, then divide by the total frequency:

Common slip: divide by Σf (the total frequency, here 20) — not by the number of rows in the table (which is only 3).

Your turn — mean from a frequency table

Estimated mean from grouped data

When data is in class intervals you don't know the exact values, so you use the midpoint of each class as a stand-in. This gives an estimate:

Why "estimated"? You don't have the real values inside each class, only the midpoint, so the answer is an approximation — not the exact mean.

Your turn — estimated mean

Data set ⇄ its average

Tap a calculation on the left, then its correct answer on the right. Work each one out in your head first.

Cumulative frequency & quartiles

Cumulative frequency is a running total of the frequencies. Plot it against the upper boundary of each class and join with a smooth curve. Then read across from key fractions of the total:

Interquartile range (IQR) = UQ − LQ. It measures the spread of the middle 50% of the data and ignores extreme values.

Box plots (box-and-whisker)

A box plot shows five numbers: the minimum, lower quartile (LQ), median, upper quartile (UQ) and maximum. The box spans LQ to UQ; the whiskers reach out to the min and max:

Reading a box plot: the box width is the IQR (spread of the middle half); the whole length min→max is the range.

Your turn — interquartile range

Scatter graphs & correlation

A scatter graph plots two variables against each other to see if they are linked. The pattern is called correlation:

• Positive correlation — as one goes up, the other goes up (points slope up ↗).
• Negative correlation — as one goes up, the other goes down (points slope down ↘).
• No correlation — points are scattered with no clear trend.

Correlation ≠ cause: a correlation shows two things move together, but it does not prove one causes the other.

Name the correlation

Positive or negative correlation?

For each pair of variables, decide whether they show positive correlation (both rise together) or negative correlation (one rises as the other falls). Tap a card, then tap the box.

Sampling

It's often impractical to survey a whole population, so we take a sample. A good sample must be representative and free of bias:

• Random sample — everyone has an equal chance of being chosen (e.g. names from a hat).
• Stratified sample — split the population into groups (strata) and sample each in proportion to its size.
• Bias — anything that makes some members more likely to be picked, making the sample unrepresentative.

Watch for bias: surveying only your friends, or only people outside a gym about exercise, gives a biased, unrepresentative sample.

Spot the bias

Your turn — stratified sample

Which average?

The whole Statistics strand

You've covered every sub-topic in the Eduqas GCSE Maths Statistics strand — from the four averages to box plots, correlation and sampling. Press Finish to see your score.