Mean (average)
Median
Mode
Range
Sum
Count
Table of Contents
Mean, median, and mode in plain English
The mean, median, and mode are the three most common measures of central tendency — different ways of summarizing a data set with a single representative value. Each one captures a different aspect of "the typical number" in your data, and knowing which to use can change the story your data tells.
The mean (arithmetic average)
The mean is what most people call "the average". To calculate it, sum all the values in the data set and divide by the count of values.
Mean = (Σx) / n
For the data set 4, 7, 9, 12, the mean is (4 + 7 + 9 + 12) / 4 = 32 / 4 = 8. The mean is intuitive and easy to compute, but it is sensitive to outliers — a single very large or very small value can pull it noticeably away from the center of the rest of the data.
The median (middle value)
The median is the value at the middle of a sorted data set. If the count is odd, it is simply the middle number. If the count is even, it is the average of the two middle numbers.
For 4, 7, 9, 12, sort gives 4, 7, 9, 12 (already sorted) and the median is (7 + 9) / 2 = 8. For 4, 7, 9, 12, 100, the median is the middle of five numbers — 9 — even though the mean has been pulled up to 26.4 by the outlier.
The mode (most frequent value)
The mode is the value that appears most often. A data set can have one mode, multiple modes (if several values tie for most frequent), or no mode at all.
For 5, 8, 12, 8, 3, 14, 8, 9, the mode is 8. Mode is the only measure of central tendency that works for non-numeric data — for example, the most common eye color in a group of people.
Which one should I use?
Use the mean when your data is roughly symmetric and outlier-free — for example, test scores, heights, or weights of a representative sample.
Use the median when your data is skewed or contains outliers — for example, household income, house prices, or response times. The median tells you what is typical without being distorted by a few extreme values.
Use the mode when you want the most popular or most frequent category — for example, the most common shoe size sold, the most frequent vote, or the most common rating in a survey.
A worked example
Consider the data set: 2, 3, 5, 8, 8, 9, 11, 12, 14
Sum = 72; count = 9; mean = 72 / 9 = 8.
Sorted (already done above), middle of 9 values is the 5th. Median = 8.
The value 8 appears twice; all others appear once. Mode = 8.
Range = 14 - 2 = 12.
This is an unusual case where mean, median, and mode all coincide — a sign of a fairly symmetric distribution. In real-world data, the three values usually differ, and comparing them is one of the quickest ways to detect skewness or unusual values.
Range, sum, and count
This calculator also returns the range (largest minus smallest, a quick measure of spread), the sum (total of all values), and the count (how many numbers you entered) so you have everything you need for a basic data summary in one place.
FAQs
The mean is the arithmetic average — add all the numbers and divide by how many there are. The median is the middle value when the numbers are sorted in order. The mode is the value that appears most often. All three are measures of central tendency, but each tells you something different about a data set.
Add all the numbers together to get the sum, then divide by the count of numbers. For example, the mean of 4, 7, 9, 12 is (4 + 7 + 9 + 12) / 4 = 32 / 4 = 8.
Sort the numbers from smallest to largest. If the count is odd, the median is the middle number. If the count is even, the median is the average of the two middle numbers. For example, the median of 3, 5, 7, 9 is (5 + 7) / 2 = 6.
The mode is the value that appears most frequently. A data set can have one mode (unimodal), two modes (bimodal), more than two modes (multimodal), or no mode at all if every value appears exactly once. Unlike mean and median, mode can also be used for non-numeric data.
The mean is useful when the data is roughly symmetric and free of extreme outliers. The median is more robust when the data is skewed or has outliers — for example, household income is usually reported as a median because a few extremely high earners would distort the mean. If you are unsure, calculate both and compare them.
The range is the difference between the largest and smallest values in the data set. It gives a quick measure of how spread out the data is. For 4, 7, 9, 12, 15 the range is 15 - 4 = 11. Range is sensitive to outliers, so it is often paired with standard deviation for a fuller picture of variability.