Mean, median and range at a glance
“Average” usually means the arithmetic mean, but it is not the only way to describe a typical value. The median, the middle value, often tells a more honest story when a few numbers are far from the rest. This calculator gives both, along with the sum, minimum, maximum and range, for up to eight numbers.
The formulas
- Mean = sum of the values ÷ number of values.
- Median: sort the values. With an odd count, it is the middle one; with an even count, it is the average of the two middle ones.
- Range = maximum − minimum.
Worked example: six test scores
The scores are 72, 85, 90, 68, 95 and 85.
- Sum: 72 + 85 + 90 + 68 + 95 + 85 = 495.
- Mean: 495 ÷ 6 = 82.50.
- Sorted: 68, 72, 85, 85, 90, 95. The two middle values are 85 and 85, so the median is 85.00.
- Range: 95 − 68 = 27.
The mean sits a little below the median because the two lowest scores, 68 and 72, are further from the center than the highest ones.
How one score moves the mean and the median
| First score | Mean | Median |
|---|---|---|
| 0 | 70.50 | 85.00 |
| 40 | 77.17 | 85.00 |
| 72 | 82.50 | 85.00 |
| 85 | 84.67 | 85.00 |
| 100 | 87.17 | 87.50 |
A single missed test, scored 0, drags the mean down by 12 points but leaves the median unchanged. That robustness is why the median is preferred for skewed data.
Mean or median?
- Use the mean when the values are fairly symmetric and you need a figure that accounts for every value, such as total points, average spending per day or the mean of repeated measurements.
- Use the median for incomes, home prices, wait times and any data with a long tail. The US Census Bureau reports median household income for exactly that reason: a small number of very high incomes would pull the mean far above what a typical household earns.
- Report both when they differ a lot: the gap itself tells readers the data are skewed.
The mode
The mode is the most frequent value. In the example, 85 appears twice and every other score once, so the mode is 85. It is most useful for categories, such as the most common shoe size sold, and less so for continuous measurements where values rarely repeat exactly.
Beyond the average
An average describes the center, not the spread. Two classes can both average 80, one with every student between 75 and 85, the other ranging from 50 to 100. The range gives a first idea of that spread; the standard deviation, which uses every value, measures it more reliably.
Tips for entering data
Choose how many values you have, then fill each field. To average more than eight numbers, compute the sums of groups of eight, then combine them: add the sums and divide by the total count. Do not average the group means unless each group has the same number of values.