Mean Median Mode Range Calculator

Mean

The word mean can have many meanings in English, and even in mathematics and statistics, its definition changes depending on the context. In its simplest form, when working with data sets, mean usually refers to the arithmetic mean — also called the average or mathematical expectation.

The arithmetic mean is calculated by adding all the values in a data set and then dividing the total by the number of values:

Mean = ^{Sum of all values}⁄_{Number of values}

This formula is almost identical for both the population mean and sample mean, with only minor differences in notation:

• Sample mean is usually written as x̄ (“x-bar”).
• Population mean is written as the Greek letter μ (mu).

Example:

10, 2, 38, 23, 38, 23, 21

Calculation:
^{10 + 2 + 38 + 23 + 38 + 23 + 21}⁄₇ = ¹⁵⁵⁄₇ ≈ 22.143

Median

The median is the middle value of a sorted data set — the point that divides the numbers into two equal halves.

Steps to find the median:

1. Arrange the numbers in ascending (or descending) order.
2. If there’s an odd number of values, the median is the middle one.
3. If there’s an even number of values, the median is the average of the two middle numbers.

Example:

2, 10, 21, 23, 23, 38, 38

Number of values: 7 (odd) → Median = 23

If we add another value:

2, 10, 21, 23, 23, 38, 38, 1027892

Number of values: 8 (even) → Median =
(23 + 23) ÷ 2 = 23

Notice that adding an extremely large number does not change the median much, but it greatly increases the mean.

Mode

The mode is the value that occurs most often in a data set.

Example:

2, 10, 21, 23, 23, 38, 38

Both 23 and 38 appear twice, so this data set is bimodal.

Mode also works for non-numerical data. For example, if a grocery store sells tortilla chips in three brands — Tostitos, Mission, and XOCHiTL — and sales are in a 3:2:1 ratio, XOCHiTL is the mode.

Range

The range is the difference between the largest and smallest numbers in a data set:

Range = Largest value − Smallest value

Example:

2, 10, 21, 23, 23, 38, 38

Range = 38 − 2 = 36

With an outlier:

2, 10, 21, 23, 23, 38, 38, 1027892

Range = 1,027,892 − 2 = 1,027,890

Like the mean, the range is affected by extreme values, so it should be interpreted carefully.

Related Calculators:
Statistics Calculator, Probability Calculator

External Resources:
Mean Median Mode Range Calculator on Calculator.net