An average is a typical value

An average is one number that stands in for a whole set of data — a "typical" value. There are three you must know, plus a measure of spread:

• Mean — add up all the values, then divide by how many there are.
• Median — put the values in order, then take the middle one.
• Mode — the value that appears most often.
• Range — a measure of spread: largest − smallest.

Memory hook: mode = most; median = middle; the range is not an average — it tells you how spread out the data is.

Finding the mean

Watch out: a single very big or very small value (an outlier) can drag the mean away from what's typical — that's when the median is often a better choice.

Your turn — the mean

Median and mode

For the median, always put the data in order first, then find the middle. For the mode, just spot the most common value.

Even number of values? The median is the mean of the middle two. For 4, 6, 9, 11 the middle two are 6 and 9, so median = (6 + 9) ÷ 2 = 7.5.

Find the median

The range measures spread

The range is not an average — it tells you how spread out the data is. A small range means the values are close together; a large range means they are widely scattered.

Comparing two sets: use an average to compare what's typical and the range to compare how consistent they are. A player with the same mean but a smaller range is more reliable.

Your turn — the range

Mean or median?

Both are "averages", but they behave differently when the data has an outlier — one value much larger or smaller than the rest.

Common mistake: people say "the mean is always the best average". Not true. Use the median when there is an outlier, because the mean gets dragged towards it. Use the mode for non-numerical data like favourite colour.

Which average is best?

Average ↔ when to use it

Tap an average on the left, then tap the situation on the right that it suits best.

Is the mean always the fairest average?

Same-size slices: same number of pupils?

Frequency tables

A frequency table records how many times each value occurs. It's a tidy way to handle lots of repeated data.

Mode from a table: the mode is the value with the highest frequency, here 1 goal (frequency 6). The total frequency (3 + 6 + 4 = 13) is how many pieces of data there are.

Your turn — reading a table

Bar charts

A bar chart shows data in separate categories using bars of equal width. The height of each bar shows its frequency. Bars have gaps between them.

Always check the axes. The gaps between bars show the categories are separate. Read the height off the vertical (frequency) axis carefully — note what each gridline is worth.

Reading the bar chart

Pictograms

A pictogram uses a symbol to stand for a number of items. You must read the key — each symbol can be worth more than one.

Common mistake: counting the symbols instead of the value. Always multiply the number of symbols by what the key says one symbol is worth.

Your turn — the pictogram

Pie charts show proportion

A pie chart shows how a whole is shared out. Each slice is a fraction of the whole circle, and the whole circle is 360°.

Common mistake: a pie chart shows proportion, not amount. Two pie charts can have identically sized slices while representing totally different totals. And every slice is a share of 360° — the angles must add to 360°.

Your turn — pie chart angle

Same-size slices: same number of pupils?

Which chart fits?

Tap the chart type that best matches each job.

Does ice cream cause swimming accidents?

Scatter graphs & correlation

A scatter graph plots two variables against each other (this is called bivariate data) to see if they are linked. The pattern of points shows the 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 pattern.

Correlation is not causation

A scatter graph can show two things rise together — but that does not prove one causes the other. There may be a hidden third factor.

Common mistake: writing "X causes Y" from a scatter graph. You can only say they are correlated (linked). Proving cause needs a fair, controlled experiment.

Reading correlation

Does ice cream cause swimming accidents?

The key ideas to know

You've covered the key ideas in the KS3 Statistics strand — averages and spread, tables and charts, and bivariate data. Press Finish to see your score.