Mean, median, and mode explained
Mean, median, and mode are the three common measures of the center of a data set. Each answers what is a typical value here in a different way. This guide explains how to find each one, with examples, and when each is the right choice.
The mean (average)
The mean is what most people call the average. Add up all the values, then divide by how many there are.
- Add every value in the data set.
- Count how many values there are.
- Divide the total by the count.
For 4, 8, 6, 10, 2: the sum is 30 and there are 5 values, so the mean is 30 ÷ 5 = 6.
The median (middle value)
The median is the middle value when the data is sorted in order. Half the values fall below it and half above.
- Sort the values from smallest to largest.
- With an odd number of values, the median is the middle one.
- With an even number, the median is the average of the two middle values.
Sorted, 2, 4, 6, 8, 10 has middle value 6. For 2, 4, 6, 8 (even count), the median is the average of 4 and 6, which is 5.
The mode (most frequent)
The mode is the value that appears most often. A data set can have one mode, several, or none at all if every value is unique.
In 3, 7, 7, 2, 9, 7, 4 the number 7 appears three times, more than any other, so the mode is 7.
When to use each one
The mean uses every value, which makes it precise but sensitive to outliers: a single very large value can pull it far from the typical case. The median ignores how extreme the outliers are and reports the true middle, which is why incomes and house prices are usually given as medians. The mode is the only one that works for non-numeric categories, such as the most common shoe size. For roughly symmetric data the mean is ideal; for skewed data the median often tells a more honest story.
- The mean is the sum of the values divided by how many there are.
- The median is the middle value of the sorted data.
- The mode is the value that occurs most often.
- The mean is sensitive to outliers; the median resists them.
- Use the median for skewed data like incomes, and the mode for categories.
Statistics tools and guides
Use the Mean Median Mode Calculator, or read the Standard Deviation Guide to measure spread.
FAQ
What is the difference between mean and median?
The mean is the arithmetic average of all values; the median is the middle value when they are sorted. The median is less affected by extreme values.
Can a data set have more than one mode?
Yes. If two or more values tie for most frequent, the data is bimodal or multimodal. If nothing repeats, there is no mode.
Which average should I use?
Use the mean for symmetric data, the median when outliers or skew are present, and the mode for the most common category or value.