Central Tendency

2nd SARA Statistics Winter School, 23-27 Jan 2026

Measures of Central Tendency

Describe the center or typical value of a dataset.


The three most common measures are:

  1. Mean (Average).

  2. Median (Middle value).

  3. Mode (Most frequent value).

Mean

The mean is calculated as the sum of all data points divided by the number of points. It’s sensitive to extreme values (outliers).


\[ \bar{X} = \frac{\displaystyle\sum_{i=1}^nx_i}{\displaystyle n} \]

Median

The median is the middle value of a sorted dataset. It is robust to outliers.

If the dataset has an even number of elements, the median is the average of the two middle values.

Mode

The mode is the most frequently occurring value in the dataset.

Problems with Mode

Unlike the mean and median, there can be no mode, one mode, or multiple modes.

Key Insights

  • Mean: Best for symmetric datasets but affected by outliers.

  • Median: Robust to outliers, useful for skewed data.

  • Mode: Describes the most common value, useful for categorical data.

Mean the Balancing Point

Effect on Mean