Mean, Median, Mode, Range Calculator

Calculate mean, median, mode, range, and geometric mean for any data set. Includes column chart and sorted data display.

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Mean, Median, Mode, and Range

These four measures describe the center and spread of a data set. Together they give a quick summary of the data's distribution without needing a full statistical analysis.

Formulas

Measure	Formula	Best For
Mean	Sum ÷ Count	Symmetric data, general average
Median	Middle value (sorted)	Skewed data, outlier resistance
Mode	Most frequent value	Categorical data, finding peaks
Range	Max − Min	Quick spread estimate
Geometric Mean	ⁿ√(x₁ × x₂ × ... × xₙ)	Growth rates, ratios

Examples

Example 1: Test Scores

Data: 72, 85, 90, 85, 78

Mean: (72 + 85 + 90 + 85 + 78) ÷ 5 = 82
Median: Sorted = 72, 78, 85, 85, 90 → middle = 85
Mode: 85 (appears twice)
Range: 90 − 72 = 18

Example 2: Skewed Data

Data: 30, 35, 32, 31, 250 (one outlier)

Mean: 75.6 (pulled up by outlier)
Median: 32 (better represents the "typical" value)

This shows why median is preferred for skewed data — the mean is misleading here.

Mean vs Median

	Mean	Median
Outlier sensitivity	Highly sensitive	Resistant
Skewed data	Misleading	More representative
Symmetric data	Equal to median	Equal to mean
Common use	GPA, test averages	Income, house prices

When There Is No Mode

If all values appear the same number of times (e.g., all unique), there is no mode. If multiple values tie for highest frequency, the data set is multimodal — all tied values are modes.

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Frequently Asked Questions

How do you find the mean, median, mode and range?

For the set 2, 5, 5, 8, 10 the mean is 6, the median is 5, the mode is 5 and the range is 8. The mean is the sum (30) divided by the count (5). The median is the middle value once the numbers are sorted. The mode is the most frequent value. The range is the largest value minus the smallest, 10 - 2 = 8.

How do you find the median of an even set of numbers?

Average the two middle values after sorting. For 3, 7, 9, 13 the two middle values are 7 and 9, so the median is (7 + 9) / 2 = 8. The median does not have to be one of the numbers in the set, and with an even count it usually is not.

Can a data set have no mode?

Yes. If every value appears exactly once, the data set has no mode. If two values tie for the highest frequency, both are modes and the set is called bimodal; three or more tied values make it multimodal. For 3, 5, 5, 7 the single mode is 5 because it is the only value that repeats.

When should you use the median instead of the mean?

Use the median when the data has outliers or is skewed, such as incomes or house prices, and the mean when the data is roughly symmetric. One extreme value pulls the mean toward it but barely moves the median, so the median gives a better picture of a typical value in lopsided data.