How to Find the Mean, Median, Mode, and Range
The mean, median, and mode are the three common measures of central tendency: each describes a "typical" value of a data set in a different way. The range is a simple measure of spread. This calculator sorts your numbers and computes all four at once.
- Mean: add all values and divide by how many there are.
- Median: sort the values; the median is the middle one. With an even count, it is the average of the two middle values.
- Mode: the value that appears most often. A set can have one mode, several modes (multimodal), or no mode if no value repeats more than the others.
- Range: the largest value minus the smallest value.
Mean = (x₁ + x₂ + … + xₙ) ÷ n Range = max − min
Worked Example
Data: 3, 7, 7, 2, 9, 4
- Sorted: 2, 3, 4, 7, 7, 9 (n = 6)
- Mean = 32 ÷ 6 = 5.333…
- Median = (4 + 7) ÷ 2 = 5.5 (even count, so average the two middle values)
- Mode = 7 (appears twice)
- Range = 9 − 2 = 7
Which Average Should You Use?
The mean uses every value but is pulled by outliers; a single very large salary can raise the mean salary of a small group a lot. The median resists outliers, which is why it is used for home prices and household income. The mode is the only measure that works for categories (such as the most common shoe size).
Frequently Asked Questions
How do you find the median with an even number of values?
Sort the values and take the average of the two middle numbers. For 2, 3, 4, 7, 7, 9, the middle values are 4 and 7, so the median is 5.5.
What if there is no mode?
If every value appears the same number of times (for example, all values are different), the data set has no mode.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, the set is bimodal or multimodal and all of those values are modes.
What is the difference between mean and average?
In everyday use, "average" usually means the arithmetic mean: the sum divided by the count. Median and mode are also types of averages.
How do outliers affect the mean and median?
Outliers can move the mean a lot because every value is included in the sum. The median depends only on the middle position, so it changes little.