Skip to content

Mean, Median, Mode, Range Calculator

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

8 numbers entered
Mean (Average)
24.25
Mean (Average)24.25
Median23
Range34
Mode8, 42 each appeared 2 times
Geometric Mean20.285005969873
Largest42
Smallest8
Sum194
Count8
Sorted Data Set: 8, 8, 15, 19, 27, 33, 42, 42

Column Chart of Values

15
8
42
27
42
33
8
19
1 8

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

MeasureFormulaBest For
MeanSum ÷ CountSymmetric data, general average
MedianMiddle value (sorted)Skewed data, outlier resistance
ModeMost frequent valueCategorical data, finding peaks
RangeMax − MinQuick spread estimate
Geometric Meanⁿ√(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

MeanMedian
Outlier sensitivityHighly sensitiveResistant
Skewed dataMisleadingMore representative
Symmetric dataEqual to medianEqual to mean
Common useGPA, test averagesIncome, 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.

Related Calculators

Percentage Calculator

Calculate percentages instantly. Find what percent of a number is, percentage increase/decrease, and more.

Fraction Calculator

Add, subtract, multiply, and divide fractions. Get results as simplified fractions, mixed numbers, and decimals.

Equivalent Fractions Calculator

Find equivalent fractions for any proper, improper, or mixed fraction. Shows the first 100 equivalent fractions.

Average Calculator

Calculate mean, median, mode, range, and standard deviation. Complete statistics for any data set.

Ratio Calculator

Simplify ratios, solve proportions, and scale ratios. Convert between ratios, decimals, and percentages.

Exponent Calculator

Calculate powers, roots, exponentials, and logarithms. Solve xⁿ, ⁿ√x, eˣ, and log expressions.

Frequently Asked Questions

What is the mean?

The mean (average) is the sum of all values divided by the count. For [2, 5, 8], the mean is (2+5+8)/3 = 5. It represents the central tendency but can be skewed by outliers.

What is the median?

The median is the middle value when data is sorted. For odd counts, it is the center value. For even counts, it is the average of the two center values. Median is resistant to outliers unlike mean.

What is the mode?

The mode is the most frequently occurring value(s). A data set can have no mode (all unique), one mode (unimodal), or multiple modes (bimodal/multimodal). For [3, 5, 5, 7], the mode is 5.

What is the range?

The range is the difference between the largest and smallest values: Range = Max − Min. It measures spread but is sensitive to outliers. For [2, 5, 8, 12], range = 12 − 2 = 10.

What is the geometric mean?

The geometric mean is the nth root of the product of n values. It is useful for growth rates and ratios. Only defined for positive numbers. For [2, 8], geometric mean = √(2×8) = 4.

When should I use median vs mean?

Use median when data has outliers or is skewed (income, house prices). Use mean when data is symmetrically distributed. Median gives a better sense of "typical" when extreme values are present.