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KS3 Mathematics · National Curriculum · Statistics
Mini-Lesson

Statistics

This mini-lesson walks you through the whole KS3 Statistics strand: the three averages (mean, median, mode) and the range; how to read and draw bar charts, pie charts, pictograms and frequency tables; and how scatter graphs show correlation between two things.

raw data the numbers a summary chart / average organise so we can compare and decide

Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Press Start when you're ready.

Averages & spread

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:

  • Meanadd 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.

Averages · the mean

Finding the mean

mean = sum of values ÷ number of valuesadd them all up, then divide by how many there are
Worked example

Five test scores: 6, 8, 5, 9, 7.

Sum = 6 + 8 + 5 + 9 + 7 = 35

Mean = 35 ÷ 5 = 7

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.

Calculate

Your turn — the mean

1A netball team scores 4, 7, 3, 10 and 6 goals in five matches. Calculate the mean number of goals per match.
goals
Hint: add the five values (4+7+3+10+6), then divide by 5.
Averages · median & mode

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.

Worked example — median

Data: 12, 7, 9, 3, 10. In order: 3, 7, 9, 10, 12.

The middle value is 9, so the median = 9.

Worked example — mode

Shoe sizes: 5, 6, 6, 7, 6, 8. The value 6 appears three times.

Mode = 6.

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.

Quick check

Find the median

?Here are seven ages: 11, 14, 12, 11, 15, 13, 12. What is the median age?
Spread · the range

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.

range = largest value − smallest valuea measure of spread, not a typical value
Worked example

Temperatures: 18, 21, 15, 24, 19 °C.

Range = 24 − 15 = 9 °C

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.

Calculate

Your turn — the range

2The heights of five plants are 22, 30, 18, 27 and 25 cm. Calculate the range of the heights.
cm
Hint: largest (30) − smallest (18).
Choosing an average

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.

Example — salaries in a small firm

Wages (£1000s): 18, 19, 20, 21, 150 (the boss).

Mean = 228 ÷ 5 = 45.6 → but nobody earns near that!

Median = 20 → a much more typical figure.

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.

Quick check

Which average is best?

?A house-price list is 180, 190, 195, 200 and 2000 (£1000s). Which average best represents a typical house?
Match it

Average ↔ when to use it

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

Tables · frequency tables

Frequency tables

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

GoalsFrequency 03 16 24
This says: 3 matches with 0 goals, 6 matches with 1 goal, 4 matches with 2 goals — 13 matches in total.

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.

Calculate

Your turn — reading a table

3In a survey, 5 people own 0 pets, 8 own 1 pet, and 7 own 2 pets. How many people were surveyed in total?
people
Hint: add the three frequencies (5 + 8 + 7).
Charts · bar charts

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.

02468 AppleBananaGrapePear Favourite fruit Frequency
Banana is the tallest bar (frequency 8), so it is the mode — the most popular fruit.

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.

Quick check

Reading the bar chart

?Using the fruit bar chart from the previous screen, how many more people chose Banana than chose Grape?
Charts · pictograms

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.

MonTueWed 📕📕📕 📕 📕📕 Key: 📕 = 2 books
Monday shows 3 symbols. Each symbol = 2 books, so 3 × 2 = 6 books on Monday.

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

Calculate

Your turn — the pictogram

4On the pictogram, the key is 📕 = 2 books. Wednesday shows 2 symbols. How many books were read on Wednesday?
books
Hint: number of symbols (2) × value of one symbol (2).
Charts · pie charts

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°.

90° 135° 135° Walk (6) Bus (9) Car (9)
24 students. Walk = 6, so its angle = (6 ÷ 24) × 360° = 90°.
slice angle = (category ÷ total) × 360°each slice is that fraction of the full 360° circle

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°.

Calculate

Your turn — pie chart angle

5In a survey of 40 people, 10 chose pizza. What angle should the "pizza" slice be on a pie chart?
°
Hint: (10 ÷ 40) × 360°.
Sort it

Which chart fits?

Tap the chart type that best matches each job.

Bivariate data · scatter graphs

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:

Revision hours → Test score → line of best fit
As revision hours go up, scores go up — this is positive 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.
Interpreting correlation

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.

Classic example

Ice-cream sales and drowning incidents both rise together over the year.

Ice cream doesn't cause drowning! The hidden factor is hot weather, which raises both.

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.

Quick check

Reading correlation

?A scatter graph shows that as outside temperature rises, sales of hot soup fall. What kind of correlation is this?
Recap

The key ideas to know

Mean: sum of values ÷ number of values

Median: order the data, take the middle value

Mode: the most common value

Range: largest − smallest (spread, not an average)

Pie chart: slice angle = (category ÷ total) × 360°

Scatter graph: positive / negative / no correlation — but correlation ≠ causation

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

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Mini-lesson complete!

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You've worked through Statistics for KS3 Mathematics. 🎉

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