Data Handling & Averages

Data handling is about collecting, organising, displaying, and interpreting information. In the GL 11+ exam, you may be asked to read charts and tables, calculate averages, and draw conclusions from data. This lesson covers all the key skills.

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Types of Data

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

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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 (how often something occurs).

Pictograms

• Use pictures or symbols to represent data.
• A key tells you what each symbol represents (e.g. one smiley face = 4 people).
• Half a symbol = half the value.

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 measured quantity.

Pie Charts

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

Tables and Tally Charts

• Tally charts use marks in groups of 5 (four lines with a diagonal across them) to record data.
• Frequency tables list the categories and their counts.

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Reading Charts and Graphs

Worked Example: Bar Chart

A bar chart shows the favourite colours of 30 children:

Colour	Frequency
Red	8
Blue	12
Green	6
Yellow	4

Questions you might be asked:

• "How many more children chose Blue than Green?" → 12 - 6 = 6
• "What fraction of children chose Red?" → 8/30 = 4/15
• "What percentage chose Yellow?" → (4/30) × 100 = 13.3% (or 13⅓%)

Worked Example: Pie Chart

A pie chart shows how 60 students travel to school.

Method	Angle	Number of students
Walk	120°	120/360 × 60 = 20
Car	90°	90/360 × 60 = 15
Bus	108°	108/360 × 60 = 18
Cycle	42°	42/360 × 60 = 7

Key formula: Number = (angle ÷ 360) × total

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Averages

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

Mean

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

Find the mean of: 4, 7, 8, 3, 8

• Sum = 4 + 7 + 8 + 3 + 8 = 30
• Number of values = 5
• Mean = 30 ÷ 5 = 6

Median

Put the values in order and find the middle one.

Find the median of: 12, 5, 8, 3, 15

• In order: 3, 5, 8, 12, 15
• Median = 8

What if there is an even number of values?

Find the median of: 4, 7, 9, 12