Data Handling and Averages

Data handling questions on the CSSE 11+ maths paper test your ability to read, interpret, and analyse data from charts, tables, and graphs. You also need to calculate averages (mean, median, mode) and understand the range. The CSSE often combines data skills with reasoning — for example, asking you to compare two data sets or explain which average is most appropriate.

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Types of Data

Type	Description	Examples
Discrete	Can only take particular values (usually whole numbers)	Number of pets, shoe size, goals scored
Continuous	Can take any value within a range	Height, weight, time, temperature

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Types of Charts and Graphs

Bar Charts

• Used for discrete or categorical data.
• Bars have equal widths and gaps between them.
• The height of each bar shows the frequency.

Line Graphs

• Used to show how data changes over time.
• Points are plotted and joined with straight lines.
• The x-axis usually shows time; the y-axis shows the quantity measured.

Pie Charts

• A circle divided into sectors (slices).
• Each sector represents a proportion of the whole.
• The whole circle = 360°.

Pictograms

• Use pictures or symbols to represent data.
• A key tells you what each symbol stands for (e.g. one symbol = 5 items).
• Part of a symbol = a fraction of the value.

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Reading Pie Charts

The key formula for pie charts:

Number = (angle ÷ 360) × total

Worked Example

A pie chart shows how 90 students travel to school:

Method	Angle
Walk	140°
Bus	100°
Car	80°
Cycle	40°

How many students walk?

• (140 ÷ 360) × 90 = 35 students

How many cycle?

• (40 ÷ 360) × 90 = 10 students

CSSE Tip: Always check that the angles add up to 360° and the numbers add up to the total.

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Averages

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

Mean

Add all the values and divide by the number of values.

Find the mean of: 6, 9, 4, 11, 5

• Sum = 6 + 9 + 4 + 11 + 5 = 35
• Number of values = 5
• Mean = 35 ÷ 5 = 7

Median

Put the values in order and find the middle one.

Find the median of: 14, 7, 3, 11, 9

• In order: 3, 7, 9, 11, 14
• Median = 9

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

Find the median of: 5, 8, 12, 15

• Middle two: 8 and 12
• Median = (8 + 12) ÷ 2 = 10

Mode

The value that appears most often.

Find the mode of: 4, 7, 2, 7, 9, 4, 7

• 7 appears three times (more than any other).
• Mode = 7

A set of data can have no mode, one mode, or more than one mode.

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Range

The difference between the highest and lowest values.

Find the range of: 3, 8, 15, 6, 11

• Range = 15 - 3 = 12

The range is not an average — it measures spread (how spread out the data is).

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Averages from a Frequency Table