Mean, Median & Mode

Three Measures of Average

Mean (Arithmetic Average)

Mean = Sum of all values ÷ Number of values

For 4, 7, 7, 9, 13: Mean = (4 + 7 + 7 + 9 + 13) / 5 = 40/5 = 8

Advantage: uses all values Disadvantage: affected by outliers (extreme values)

Median (Middle Value)

Arrange data in order, then find the middle value.

Odd number of values → middle one Even number of values → mean of the two middle values

For 3, 5, 5, 8, 9, 12 (6 values): Median = (5 + 8) / 2 = 6.5

Best when: data has outliers or is skewed

Mode (Most Frequent)

The value that appears most often. A data set can have no mode, one mode, or several modes.

For 4, 7, 7, 9, 13 → Mode = 7

Best when: dealing with categorical data

Measures of Spread

Range = Maximum − Minimum For 12, 7, 19, 3, 15 → Range = 19 - 3 = 16

Interquartile Range (IQR) = Q3 − Q1 (middle 50% of data) — less affected by outliers than range.

Which Average to Use?

Situation	Best average
Symmetric data, no outliers	Mean
Skewed data or outliers	Median
Categorical data	Mode