Mode, Median, and Mean: How to Choose

Mode, median, and mean are the three most common measures of central tendency used to summarize a dataset. Knowing which one to pick is the first step toward a summary that matches the shape of your data.

Arithmetic mean

The mean is obtained by dividing the sum of all observations by the number of observations. It is the most reliable measure of central tendency for continuous, roughly symmetric data — but it is sensitive to extreme values (outliers).

Example: If five students’ test scores are 70, 75, 78, 82, and 90, the mean is (70+75+78+82+90)/5 = 79.

Median

The median is the middle value of the sorted dataset. Because it is unaffected by extreme values, it is preferred over the mean when the distribution is skewed.

• If the number of observations is odd: the median is the middle value.
• If the number of observations is even: it is the mean of the two middle values.

Mode

The mode is the most frequently occurring value in a dataset. It is the most meaningful measure of central tendency for categorical (nominal) data. A dataset may be unimodal, multimodal, or have no mode at all.

Which one — and when?

• Symmetric, continuous data: the mean is the most informative measure.
• Skewed data or outliers: the median better reflects the center of the distribution.
• Categorical data: the mode highlights the dominant category.

In practice these three measures are usually reported together: a visible gap between mean and median is a strong signal that the distribution is skewed and calls for additional dispersion measures (e.g., standard deviation, interquartile range).