Statistics

Statistics involves collecting, organising, presenting and interpreting data. At KS3 you will calculate measures of average and spread, construct and interpret a range of charts, and use scatter graphs to explore relationships between variables.

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Types of Data

Type	Description	Examples
Qualitative (categorical)	Non-numerical	Colours, names, types
Quantitative discrete	Numerical, exact values	Number of siblings, shoe size
Quantitative continuous	Numerical, any value in a range	Height, temperature, time
Grouped data	Continuous data in class intervals	10 ≤ h < 20

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Measures of Central Tendency

Measure	Definition	Best used when…
Mean	Sum of all values ÷ number of values	No extreme outliers
Median	Middle value when data is ordered	Data has outliers
Mode	Most frequent value	Categorical data or finding the most common

Example data: 4, 7, 3, 9, 7, 11, 4, 7, 2 → Ordered: 2, 3, 4, 4, 7, 7, 7, 9, 11

• Mean = (2+3+4+4+7+7+7+9+11) ÷ 9 = 54 ÷ 9 = 6
• Median = 5th value of 9 = 7
• Mode = 7 (appears 3 times)

For n data values: if n is odd, median = ((n+1)/2)th value; if n is even, median = mean of the two middle values.

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Measures of Spread

Range = largest value − smallest value

Example: Range of {2, 3, 4, 4, 7, 7, 7, 9, 11} = 11 − 2 = 9

Outliers are unusually large or small values. They affect the mean significantly but have less impact on the median.

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Frequency Tables

Score	Frequency (f)	f × Score
1	5	5
2	8	16
3	12	36
4	9	36
5	6	30
Total	40	123

Mean from frequency table = sum(f × x) ÷ sum(f) = 123 ÷ 40 = 3.075

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Grouped Frequency Tables

When data is grouped, use the midpoint of each class to estimate the mean.

Height h (cm)	Midpoint	Frequency (f)	f × midpoint
150 ≤ h < 160	155	3	465
160 ≤ h < 170	165	10	1650
170 ≤ h < 180	175	14	2450
180 ≤ h < 190	185	8	1480
190 ≤ h < 200	195	5	975
Total		40	7020

Estimated mean = 7020 ÷ 40 = 175.5 cm Modal class = 170 ≤ h < 180 (highest frequency).

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Representing Data