Statistics Cheat Sheet

Statistics Cheat Sheet

Quick Revision

Statistics begins with the three measures of central tendency — the mean, the median and the mode — each a different way of finding the "centre" of a set of numbers.

1. Mean (Average)

Mean = Sum of all values / Number of values

Example

For 4, 8, 10, 14: Mean = (4 + 8 + 10 + 14) / 4 = 36 / 4 = 9.

2. Median (Middle Value)

Arrange the values in order, then:

• Odd number of values → the middle value.
• Even number of values → the average of the two middle values.

Example

For 3, 5, 7, 9, 11 (odd, 5 values): the median is the 3rd value, 7. For 4, 8, 10, 14 (even): median = (8 + 10) / 2 = 9.

3. Mode (Most Frequent)

The mode is the value that appears most often. A set can have one mode, more than one, or none.

Example

For 2, 3, 3, 5, 7, 3, 8: the mode is 3 (it appears three times).

4. Range

Range = Highest value − Lowest value

For 4, 8, 10, 14: Range = 14 − 4 = 10.

5. Empirical Relationship

For a moderately skewed set, the three measures are linked by:

Mode = 3 × Median − 2 × Mean

6. Exam Quick Tips

• Always sort the values before finding the median.
• For an even count, the median is the average of the two middle values.
• A set can have no mode (all values different) or several.
• Remember the empirical link: Mode = 3 Median − 2 Mean.

Keep revising with the rest of the Maths section:

• All Maths topics
• Probability Cheat Sheet
• Average Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.