Mean, the usual average
The average most people mean is the arithmetic mean: add the numbers and divide by how many there are. For the scores 78, 85, 90, 73, and 88, the sum is 414. There are 5 scores, so the mean is 414 ÷ 5 = 82.8. One low score pulls the mean down. Replacing 73 with 93 would raise the sum by 20 and the mean by 4, to 86.8. Every value has the same influence. If some scores should count more than others, that is a weighted average, not this average.
Type the numbers with spaces or semicolons between them. A thousands separator has to stay attached to its number, as in 1,200 1,450, because a comma followed by a space starts a new value. Decimals use a point: 82.5 is eighty-two and a half, not eighty-two thousand five hundred.
Worked example, including the median
The median is the middle value after sorting, and it ignores how extreme the ends are. Sort 78, 85, 90, 73, 88 and you get 73, 78, 85, 88, 90. The middle of five values is 85. The mean was 82.8, so the low 73 pulled the mean 2.2 points below the median.
- Sum: 78 + 85 = 163; 163 + 90 = 253; 253 + 73 = 326; 326 + 88 = 414.
- Mean: 414 ÷ 5 = 82.8.
- Median: the third of the sorted list is 85.
- Minimum 73, maximum 90, range 17.
When the mean is the wrong summary
With an even count, the median is the mean of the two middle numbers. The median of 4, 1, 3, and 2 is the mean of 2 and 3 after sorting, which is 2.5. The mean of those four numbers is also 2.5, but that agreement is a coincidence of this particular list. One very large value, such as a single $10,000 invoice in a stack of $20 invoices, will drag the mean up and leave the median near the typical invoice. Report the one the question asked for. “Average” with no other word almost always means the mean. “Typical” often means the median.
The mean does not say how spread out the numbers are. Two classes can share a mean of 82 while one is a tight cluster and the other runs from 40 to 100. The standard deviation calculator measures that spread. This page stops at the center, the sum, and the extremes.