Mean, median, mode & range

The three averages each describe the centre of a data set in a different way; the range measures how spread out it is.

• Mean — add up all the values, divide by how many there are.
• Median — put the values in order, take the middle one.
• Mode — the value that appears most often.
• Range — largest value − smallest value (a measure of spread, not an average).

Don't mix them up: the median needs the data ordered first, and the range is a measure of spread — it is not an average.

Your turn — the mean

Your turn — the median

Which average is this?

Your turn — the mode

Your turn — the range

Averages from a frequency table

A frequency table records how many times each value occurs. To find the mean, add an fx column (value × frequency), then divide by the total frequency.

Common slip: divide by the total frequency (10), not by the number of different values (3). Every repeat counts.

Grouped data & the estimated mean

When data is in class intervals (e.g. 0–10, 10–20) we don't know the exact values, so we use the midpoint of each class as a stand-in. The mean we get is an estimate.

Why "estimated"? Using the midpoint assumes values are evenly spread inside each class, which usually isn't exactly true — so the answer is an estimate.

Your turn — estimated mean

Cumulative frequency & the median

A cumulative frequency is a running total of the frequencies. Plotting cumulative frequency against the upper boundary of each class gives an S-shaped curve you can read the median and quartiles from.

Reading the median: go to ½n on the vertical axis (not on the data axis), read across to the curve, then straight down to the value.

Box plots, quartiles & IQR

A box plot summarises a data set with five numbers: minimum, lower quartile (LQ), median, upper quartile (UQ) and maximum. The interquartile range measures the spread of the middle half:

Why the IQR? Unlike the range, it ignores the extreme minimum and maximum, so a single outlier doesn't distort it.

Your turn — interquartile range

Statistic ⇄ its value

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

Scatter graphs & correlation

A scatter graph plots two variables together to show whether they are related. The pattern of points describes the correlation:

• Positive — as one goes up, the other goes up (points slope up).
• Negative — as one goes up, the other goes down (points slope down).
• No correlation — no clear pattern.

Correlation is not cause: a strong correlation does not prove one variable causes the other — they may just be linked to something else.

Name the correlation

Sampling

A population is the whole group you're interested in; a sample is the smaller part you actually collect data from. A good sample is random and representative, so conclusions can be generalised to the population.

• Random sample — every member of the population has an equal chance of being chosen.
• Bias — a sample that is not representative gives misleading results.
• Bigger samples are generally more reliable, but cost more to collect.

Why sample? Surveying an entire population (a census) is often too slow or expensive, so a well-chosen sample lets us estimate results efficiently.

Average or spread?

Some statistics describe the centre of the data; others describe the spread. Tap a statistic, then tap the box it belongs in.

The whole Statistics strand

You've covered the whole Statistics strand of Edexcel 1MA1. Press Finish to see your score.