Average Calculator
The average calculator gives the mean, median, mode, range, count and sum of a list, plus weighted averages, averages of percentages, and the score you need on the tests left.
Mean (average)
- Mean (average) Sum of 680 divided by 8 values.
- 85
- Median Halfway between the two middle values once sorted, the 4th and 5th: (85 + 88) / 2.
- 86.5
- Sorted
- 70, 78, 80, 85, 88, 92, 92, 95
- Mode The value that appears most often: 2 times.
- 92
- Range From 70 to 95.
- 25
- Count
- 8
- Sum
- 680
- Geometric mean The nth root of the product. The right average for growth rates and ratios that compound.
- 84.6127
- Harmonic mean The count divided by the sum of reciprocals. The right average for speeds over equal distances.
- 84.2105
- The mean is below the median, pulled down by the low values.
How the Average Calculator works
An average is one number that stands in for a list. Most of the time it means the mean: add the values and divide by how many there are. For the default list, 85, 92, 78, 92, 88, 70, 95 and 80, the sum is 680 over 8 values, so the mean is 85. The median is the middle once sorted; with eight values it sits halfway between the 4th and 5th, 85 and 88, so 86.5. The mode is the most frequent value, 92, and the range is 95 - 70 = 25. Any mean calculator gives the first of these. The median is the one to trust when a few extreme values drag the mean away from the typical case.
Weighted average. When the values do not count equally, multiply each by its weight, add those up and divide by the total weight. A course graded 20% homework, 30% midterm and 50% final, with scores of 90, 85 and 72, has a weighted average of (90 x 20 + 85 x 30 + 72 x 50) / 100 = 79.5. The plain mean of the three scores is 82.33, which overstates the grade because the weakest score carries half the weight. The weights are relative: 2, 3, 5 gives the same answer.
Why averaging percentages is a trap. Three classes pass 90% of 20 students, 75% of 40 and 60% of 200. The plain mean of the rates is 75%. Count the students instead: 18 + 30 + 120 = 168 passed out of 260, which is 64.62%. The plain mean treats a class of 20 as if it were as big as a class of 200. The correct average of percentages with different bases is the weighted average with the bases as weights, which is the same as pooling the counts. Only when every percentage is out of the same number do the two agree.
The score you need. With every test counted equally, the average needed on the tests left is (target x total tests - points so far) / tests left. The default eight scores average 85; to finish at 87 after two more tests takes (87 x 10 - 680) / 2 = 95 on each. Above the maximum score, the target is out of reach; at zero or below, it is already secured.
Average Calculator FAQ
How do you calculate an average?
Add the numbers and divide by how many there are. The average of 85, 92, 78, 92, 88, 70, 95 and 80 is 680 / 8 = 85. That is the mean; the median (the middle value) and the mode (the most common value) are the other two common averages.
How do you calculate a weighted average?
Multiply each value by its weight, add the products, and divide by the sum of the weights. Scores of 90, 85 and 72 weighted 20, 30 and 50 give (1,800 + 2,550 + 3,600) / 100 = 79.5.
Can you average percentages?
Only if they are all out of the same base. Otherwise pool the counts: 90% of 20, 75% of 40 and 60% of 200 is 168 out of 260, or 64.62%, while the plain mean of the three rates is 75%. Pooling is the same as a weighted average with the bases as weights.
When is the median better than the mean?
When the data are skewed or have extreme values. One very large value pulls the mean toward it but moves the median by at most one position, which is why incomes and house prices are usually reported as medians.