Understanding Mean, Median, and Mode

What Are Mean, Median, and Mode?

In statistics, the mean, median, and mode are measures of central tendency that help us understand data distributions.

• Mean: The average of a set of numbers, calculated by dividing the sum of all values by the number of values.
• Median: The middle value in a data set when the numbers are arranged in order. If there is an even number of observations, the median is the average of the two middle numbers.
• Mode: The number that appears most frequently in a data set. A set may have one mode, more than one mode, or no mode at all.

Calculating Mean, Median, and Mode

Mean

For a data set $x_1, x_2, \ldots, x_n$, the mean $\bar{x}$ is calculated as:

$$\bar{x} = \frac{x_1 + x_2 + \cdots + x_n}{n}$$

Median

• Odd number of data points: The median is the middle number.
• Even number of data points: The median is the average of the two middle numbers.

Mode

The mode is the value that appears most frequently in the data set.

Examples

Example 1: Find the Mean, Median, and Mode

Consider the data set: 3, 7, 7, 2, 5

Example 2: Find the Median

Consider the data set: 8, 3, 5, 12