Mean, Median, Mode and Range
6 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
An average is a single number that stands for a whole list. There are three common averages (mean, median and mode) and each answers a slightly different question.
How to find each one
Use the data set 2, 3, 3, 5, 7, 10.
- Mean: add and divide by the count. 30 ÷ 6 = 5.
- Median: sort the list and take the middle. With six values, average the middle two: (3 + 5) ÷ 2 = 4.
- Mode: the most frequent value: 3.
- Range: largest minus smallest: 10 − 2 = 8.
Check with the statistics calculator.
Which average should I use?
| Average | Best for | Weakness |
|---|---|---|
| Mean | Symmetrical data (test scores, heights) | Pulled by outliers |
| Median | Skewed data (income, house prices) | Ignores the size of extreme values |
| Mode | Categories, most popular option | May not exist or may be several |
The effect of an outlier
Replace the 10 with 100: the set 2, 3, 3, 5, 7, 100 has a mean of 20 but the median is still 4. The mean jumped by 15 while the median did not move, which is why news reports often quote the median income.
Spread: range and standard deviation
Two classes can have the same mean and very different spread. The range is a quick measure; the standard deviation is more informative because it uses every value. For 2, 3, 3, 5, 7, 10 the sample standard deviation is about 3.03. In a bell-shaped data set roughly 68% of values lie within one standard deviation of the mean.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Find the mean and median of 12, 15, 11, 20, 17, 15, 9.
Show answer
Mean (average): 14.14285714 · Median: 15
- What is 35% of 240?
Show answer
35% of 240: 84
- How many ways can 3 medals be awarded among 8 runners?
Show answer
Combinations C(8, 3): 56 · Permutations P(8, 3): 336
Frequently asked questions
What if there are two middle numbers?
Take their average to get the median.
Can a data set have no mode?
Yes, if every value appears once.
Should I use sample or population standard deviation?
Use sample (divide by n − 1) when your data is a subset of a larger group, which is the normal case.
How do I find a weighted average?
Multiply each value by its weight, add them, and divide by the total weight.
Try it yourself
Statistics CalculatorMean, median, mode, range, variance and standard deviation for any list of numbers.
Percentage CalculatorFind a percent of a number, percent change, and increases or decreases.Permutation and Combination CalculatorFind nPr, nCr, factorials and counts with repetition.Keep learning
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