Mean, Median, Mode Calculator

How Mean, Median, and Mode Are Calculated

These three measures of central tendency describe the “center” of a data set, each in a different way.

Mean (Average): Mean = Sum of all values / Count of values

Median (Middle Value): Sort values in order. If count is odd, take the middle value. If even, average the two middle values.

Mode (Most Frequent): The value that appears most often. A dataset can have no mode, one mode, or multiple modes.

Worked Example: Data set: 4, 7, 7, 9, 13, 15, 15, 15, 21

• Mean = (4+7+7+9+13+15+15+15+21) / 9 = 106 / 9 = 11.78
• Median = middle value (5th of 9) = 13
• Mode = 15 (appears 3 times)

When to Use Each:

• Mean: Symmetric distributions without outliers, exam scores, heights, temperatures
• Median: Skewed data or data with outliers, income, house prices, response times
• Mode: Categorical data or finding most common occurrence, shoe size, favorite color

Outlier Effect Example: Salaries: $30k, $32k, $35k, $31k, $500k

• Mean = $125.6k: misleading (skewed by CEO salary)
• Median = $32k: better reflects typical employee
• Mode = none

Reading the gap between mean and median: The distance between the mean and the median is the quickest test of whether a data set is lopsided. In the first example the mean is 11.78 and the median is 13, so they sit close together and either one describes the data reasonably. In the salary example the mean is $125.6k against a median of $32k, and that four-fold gap is the whole story: one value is dragging the average away from everybody else.

When the mean lands above the median, the long tail points to the right, which statisticians call positive skew. Below the median means the tail points left. Equal means the data is balanced. None of this needs a standard deviation to see, which is why it is worth checking first.

Range is the crudest measure of spread, just the largest value minus the smallest. For the first example that is 21 − 4 = 17. It is easy to compute and easy to fool: a single extreme value sets it on its own, and it says nothing about how the values in between are distributed. Standard deviation, which weighs every value’s distance from the mean, is the proper measure, and there is a separate calculator for it linked below.