Key Stage 3 maths · Statistics

KS3 averages, charts and scatter graphs: a guide for parents

Statistics is about collecting data, showing it clearly and deciding what it says. In Years 7 to 9 pupils compare sets of data using averages and the range, draw and interpret tables and charts for different kinds of data, think about outliers, and use scatter graphs to describe how two things are related, building on the pie charts, line graphs and mean from primary school.

Averages, charts and scatter graphs, explained

Data comes in different kinds, and the kind decides the chart. Categorical data is sorted into groups, such as favourite pets, and is shown in frequency tables, pictograms, bar charts and pie charts. Numerical data is either discrete (it can only take certain values, such as the number of siblings or shoe sizes) or continuous (measured, such as height or time). Pupils draw vertical line or bar charts for numerical data, grouped into class intervals such as 0 ≤ t < 10 when there is a wide spread of values. Pie charts show shares of a whole, with each sector’s angle found from 360° divided by the total, so 24 pupils give 15° per pupil.

An average is a single number that stands for a whole set. The mode is the most common value, the median is the middle value when the data is in order (or the halfway point between the two middle values), and the mean is the total divided by the number of values. Each is useful in a different situation. The mode suits categories, such as the most popular shoe size. The median is hardly affected by extreme values. The mean uses every value but is pulled by extremes. Pupils also find averages from a frequency table: for the mean, each value is multiplied by its frequency, the results are added, and the total is divided by the sum of the frequencies.

Averages do not tell the whole story, so pupils also measure spread. The range is the largest value minus the smallest. A small range means the values are close together and a large range means they are widely scattered. Pupils compare two sets of data using one average and one measure of spread, writing a sentence in context, such as “Class A’s mean is higher, but its range is greater, so its results are less consistent”. They also consider outliers, values far from the rest, and decide whether an outlier is a mistake to correct or a real value to keep.

Scatter graphs show two measurements for each person or object, such as height and arm span, one on each axis, with one point per pair. If the points rise from left to right, there is positive correlation. If they fall, the correlation is negative, and if there is no pattern there is no correlation. The closer the points lie to a straight line, the stronger the link. Many schools also teach drawing a line of best fit by eye and using it to estimate a missing value. The key lesson is that correlation is not the same as cause: ice cream sales and sunburn rise together, but one does not cause the other.

Words your child will hear

Mean: The total of all the values divided by how many values there are.
Median: The middle value when the data is written in order.
Mode: The value or category that occurs most often.
Range: The difference between the largest and smallest values. It measures spread.
Outlier: A value that is much bigger or smaller than the rest of the data.
Frequency: How many times a value or category occurs.
Correlation: The kind of link between two variables shown on a scatter graph: positive, negative or none.

What the National Curriculum says

In Key Stage 3, pupils should be taught to:

Describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)
Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
Describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Seven pupils record how many minutes their journey to school takes: 7, 4, 10, 6, 31, 6, 9. Find the mode, median, range and mean, and say what the 31 does to the averages.

Put the values in order first. This makes the mode, the median and the range easy to see.
```
4, 6, 6, 7, 9, 10, 31
```
Mode: 6 appears twice and everything else once. Median: with 7 values, the middle is the 4th, which is 7. Range: largest minus smallest.
```
Mode = 6
Median = 7
Range = 31 − 4 = 27
```
Mean: add all the values, then divide by how many there are.
```
Total = 4+6+6+7+9+10+31 = 73
Mean = 73 ÷ 7 = 10.4 (1 d.p.)
```
The 31 is an outlier. Without it, the total is 42 for 6 values, giving a mean of 7, a median of 6.5 and a range of 6. The median changes a little but the mean and the range change a lot.
The mean of 10.4 is higher than six of the seven journeys, so it is not a good picture of a typical journey. The median of 7 is a fairer summary.

Mode 6, median 7, range 27 and mean 10.4 minutes. The outlier of 31 pulls the mean up, so the median describes a typical journey better.

Common mistakes and how to help

Finding the median without putting the data in order

The “middle” of the list as written is not the middle of the values. Pupils take the 4th number from the original, unordered list.

What helps: Always rewrite the data from smallest to largest. For an even number of values, find the number halfway between the two middle ones.

Giving the frequency as the mode

In a frequency table, the biggest number in the “frequency” column is the count, not the value. A pupil writes “the mode is 12” when the mode is the shoe size that has a frequency of 12.

What helps: Ask “Which value occurs most often?” and point to the label, not the count. The mode is the item that is most popular, not how popular it is.

Writing the range as the biggest number

In everyday speech, “range” can mean the top of something, and the biggest value is easy to spot.

What helps: Range measures spread, so it compares two values. Largest minus smallest is the length of the stretch of number line the data covers.

Assuming correlation means one thing causes the other

A clear pattern on a scatter graph feels like an explanation, and the news often presents links this way.

What helps: Ask “What else could explain both?” Hot weather could explain ice cream sales and sunburn. Describe what the graph shows, not why.

How to help at home

Collect a small data set. Ask each member of the family or a few friends something they can count or measure, such as the number of messages sent in a day or the length of a hand span. Find the mode, median, mean and range together.
Draw a scatter graph from real measurements. Measure each person’s height and arm span, plot the pairs and describe the correlation. Is there an outlier? Does a line of best fit help predict one measurement from the other?
Read charts in the news. When a chart appears in a newspaper or on a screen, check the axes. Does the vertical axis start at zero? Is a pie chart showing percentages that add to 100? Spotting misleading charts is a useful skill.
Compare two groups. Compare the times it takes two people to do the same task five times. Use one average and the range to decide who is faster and who is more consistent.

Builds on

Year 6: Pie charts, line graphs and the mean

Leads on to

Key Stage 4: Sampling, trends and correlation
Key Stage 4: Histograms and box plots

Everything in Key Stage 3 maths

Updated 20 October 2026.