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Calculator Answers

Mean, Median, Mode & Range Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A mean median mode calculator is a statistical utility that computes the core measures of central tendency for a given set of numerical data. The mean is the mathematical average calculated by dividing the sum of values by the count; the median is the middle value when the dataset is sorted in numerical order; and the mode is the value that appears most frequently. The calculator also computes secondary statistics such as range, sum, count, minimum, and maximum. Students, statisticians, and researchers use this tool to quickly summarize numerical datasets and analyze data distributions.

Use this as a quick mean calculator, or find the median, mode, and range of any data set. Paste or type a list of numbers, separated by commas, spaces, or new lines.

See also: Average Calculator, IQR Calculator, and Variance Calculator.

Quick Answer

Calculate mean, median, mode, range, and other basic statistics for any dataset. Paste your numbers to see the statistical summary and step-by-step arithmetic.

Separate values with commas, spaces, or new lines. Decimals and negative numbers are supported.

Step by step

  1. Sort: 4, 7, 7, 9, 12
  2. Sum: 4 + 7 + 7 + 9 + 12 = 39
  3. Mean: 39 / 5 = 7.8
  4. Median: middle value at position 3 = 7
  5. Mode: 7 appears 2 times
  6. Range: 12 − 4 = 8
Summary statistics

Mean

7.8

Median 7 · Mode 7 · Range 8

Count5
Sum39
Mean7.8
Median7
Mode7
Minimum4
Maximum12
Range8
Sorted values4, 7, 7, 9, 12
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Examples

4, 7, 7, 9, 12

mean 7.8 · median 7 · mode 7 · range 8

2, 4, 6, 8

mean 5 · median 5 · no mode · range 6

1, 2, 2, 3, 3, 4

mean 2.5 · median 2.5 · modes 2 and 3 · range 3

How it works

The calculator parses every number in the list, sorts them, and then computes the standard descriptive statistics: mean, median, mode, and range. It also shows the count, sum, minimum, and maximum.

Mean

mean = sum / count

Median

Sort the values. If the count is odd, take the middle value. If the count is even, take the average of the two middle values.

Mode

The value or values that appear most often. If every value appears the same number of times, there is no mode.

Range

range = max − min

Learn the concept

These guides explain the idea this tool computes, with worked examples and the distinctions readers most often trip over.

What Is Mean in Math? The definition, the formula and why an outlier moves the mean but not the median.What Is Range in Math? Maximum minus minimum, and the other meaning the word carries for functions.

What is a mean median mode calculator?

A mean median mode calculator summarizes a list of numbers with the standard measures of central tendency and spread. It is the everyday workhorse of descriptive statistics, useful for homework, lab reports, simple data analysis, and quick sanity checks on a spreadsheet column.

How the calculator works

Enter your numbers in the input area, separated by commas, spaces, or new lines. The calculator:

  • Parses every number and ignores blank entries.
  • Sorts the values from smallest to largest.
  • Computes count, sum, mean, median, mode, and range.
  • Reports the minimum, maximum, and the sorted list.
  • Shows a step by step trace of the calculation.
  • Flags any token that is not a number so you can fix typos.

How to find the mean

Add up every value and divide by the count. The mean is also called the arithmetic average. For the default data set 4, 7, 7, 9, 12 the sum is 39 and the count is 5, so the mean is 39 ÷ 5 = 7.8.

How to find the median

Sort the values from smallest to largest. If the count is odd, the median is the single middle value. If the count is even, the median is the average of the two middle values. The median splits the data set in half, with the same count of values above and below it.

How to find the mode

Count how many times each value appears. The value or values with the highest count are the modes. If every value appears the same number of times, there is no mode. Data sets can be unimodal (one mode), bimodal (two), or multimodal (more than two).

How to find the range

Subtract the smallest value from the largest. Range is the simplest measure of spread, but it only uses two values, so it can be very sensitive to outliers. For a more stable measure of spread, look at the standard deviation.

Mean vs median vs mode

All three describe central tendency, but they react to the shape of the data differently:

  • Mean is the arithmetic average. It uses every value and is sensitive to outliers and skew.
  • Median is the middle of the sorted data. It is robust to outliers and often more representative for skewed distributions.
  • Mode is the most common value. It highlights peaks in the distribution and can sit anywhere relative to the mean and median.

For a deeper look at spread, the standard deviation calculator and the variance calculator go beyond range. For comparing a single value to a distribution, see the z score calculator.

Worked examples

  • 4, 7, 7, 9, 12: mean 7.8, median 7, mode 7, range 8
  • 2, 4, 6, 8: mean 5, median 5, no mode, range 6
  • 1, 2, 2, 3, 3, 4: mean 2.5, median 2.5, modes 2 and 3, range 3

Common mistakes

  • Forgetting to sort the data before finding the median. The middle position only makes sense in sorted order.
  • Reporting a mode when every value appears once. If the data set has no repeats, there is no mode.
  • Reporting only one mode when several values tie for the highest frequency. List every tied value.
  • Mixing up mean and median in a skewed data set. The two can differ a lot when extreme values stretch one side of the distribution.
  • Confusing range with standard deviation. Range only uses the smallest and largest values; standard deviation uses every value.

Related tools

Note. This calculator uses standard descriptive statistics formulas. Teachers, schools, or textbooks may format steps differently, but the core mean, median, mode, and range values should match standard arithmetic.

Related Calculators

More tools from Education

Average CalculatorCalculate the arithmetic mean of any list of numbers, with the median, mode, range and weighted average alongside it.IQR CalculatorFind the interquartile range, quartiles Q1, Q2, Q3, and identify outliers using the 1.5×IQR rule.Variance CalculatorCompute sample and population variance, mean, count, and standard deviation from a list of numbers.Standard Deviation Calculator – Variance & SDUse this sd calculator to compute sample and population standard deviation, variance, mean, and count from a list of numbers.

Frequently asked questions

Add up every value in the data set and divide by the number of values. For example, for 4, 7, 7, 9, 12: the sum is 39 and the count is 5, so the mean is 39 ÷ 5 = 7.8. The mean is also called the arithmetic average.

Sort the values from smallest to largest. If there is an odd number of values, the median is the single middle value. If there is an even number of values, the median is the average of the two middle values. For 4, 7, 7, 9, 12 the median is 7 (the third value). For 2, 4, 6, 8 the median is (4 + 6) ÷ 2 = 5.

The mode is the value that appears most often. For 4, 7, 7, 9, 12 the mode is 7 because it appears twice and every other value appears once. A data set can have more than one mode if multiple values tie for the highest count. If every value appears once, the data set has no mode.

Subtract the smallest value from the largest. For 4, 7, 7, 9, 12 the range is 12 − 4 = 8. Range is a quick measure of how spread out the data is, although it is sensitive to extreme values at either end.

All three are measures of central tendency, but they answer slightly different questions. The mean is the arithmetic average. The median is the middle value once the data is sorted. The mode is the most common value. The mean is sensitive to extreme values; the median is not; the mode highlights the most frequent value, which can be anywhere in the distribution.

In everyday language, the word average usually means the arithmetic mean. In statistics, average is a broader term that can include the median or mode depending on context. This calculator labels the arithmetic average as the mean and shows the median and mode alongside it.

Yes. If two or more values tie for the highest frequency, every tied value is a mode. A data set with two modes is called bimodal, and one with several modes is multimodal. The calculator lists every mode in sorted order.

Yes. If every value appears the same number of times (for example, every value appears once), there is no most frequent value, so there is no mode. The calculator displays "No mode" in that case.

They lower the mean the same way positive numbers raise it. The arithmetic works the same: add up all values and divide by the count. The mean is sensitive to extreme values in either direction, so a few very negative numbers can pull the mean below the median.

Use the median when the data has outliers or a skewed distribution, since the median is not pulled by extreme values the way the mean is. Income, home price, and reaction-time data are common cases where the median is more representative than the mean.