Data Handling and Statistics

Data handling and statistics questions appear on both stages of the SET 11+ maths papers. You will need to read and interpret tables, charts, and graphs, and calculate averages (mean, median, mode, and range). On Stage 2, you must show your working when calculating averages. This lesson covers all the skills you need.

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Types of Charts and Graphs

Type	Best for
Bar chart	Comparing categories
Pie chart	Showing proportions of a whole
Line graph	Showing change over time
Pictogram	Simple comparisons using pictures
Tally chart	Recording data during collection

SET Tip: Read the title, axis labels, and scale before answering any questions about a chart.

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Reading Charts and Tables

When reading any chart or table:

1. Read the title — what does this chart show?
2. Check the axes — what do the x-axis and y-axis represent?
3. Check the scale — does each square represent 1, 2, 5, 10, or something else?
4. Read carefully — some questions ask for the difference between two values, not just a single value.

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Averages

An average is a single number that represents a set of data. There are three types of average:

Mean

The mean is the most common average. Add all the values, then divide by how many values there are.

Mean = total of all values ÷ number of values

Worked Example 1

Find the mean of: 12, 8, 15, 9, 6

• Total = 12 + 8 + 15 + 9 + 6 = 50
• Number of values = 5
• Mean = 50 ÷ 5 = 10

Median

The median is the middle value when the data is arranged in order.

Worked Example 2

Find the median of: 14, 7, 22, 3, 18

• In order: 3, 7, 14, 18, 22
• The middle value is 14

For an even number of values, the median is the mean of the two middle values.

Find the median of: 5, 9, 12, 16

• Two middle values: 9 and 12
• Median = (9 + 12) ÷ 2 = 10.5

Mode

The mode is the value that appears most often. There can be more than one mode, or no mode at all.

Find the mode of: 4, 7, 2, 7, 5, 4, 7

• 7 appears three times — more than any other value.
• Mode = 7

Range

The range tells you how spread out the data is.

Range = highest value - lowest value

Find the range of: 14, 7, 22, 3, 18

• Range = 22 - 3 = 19

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Using the Mean to Find a Missing Value

Worked Example 3