Average calculator: mean, median, mode and range
Paste a column from a spreadsheet or type numbers separated by commas, spaces or new lines. Switch on weights to average grades by category.
The short answer
The average (mean) is the sum of the numbers divided by how many there are. For 85, 92, 78, 92 and 88 that is 435 ÷ 5 = 87. The median is the middle value once sorted (88), the mode is the most frequent (92), and the range is max minus min (14).
How it is calculated
Mean = sum of values ÷ number of values
Median = the middle value after sorting; with an even count, the mean of the two middle values
Mode = the value that appears most often (there can be several, or none)
Range = largest − smallest
Weighted average = Σ(value × weight) ÷ Σ(weight)
Worked example
A class grade weights tests 40%, homework 35% and the final exam 25%. A student averages 92 on tests, 85 on homework and 78 on the final exam.
- Tests: 92 × 40 = 3,680
- Homework: 85 × 35 = 2,975
- Final exam: 78 × 25 = 1,950
- Weighted average: 8,605 ÷ 100 = 86.05
The course grade is 86.05, not the plain average of 85.
Quick reference table
| Numbers | Mean | Median | Mode | Range |
|---|---|---|---|---|
| 85, 92, 78, 92, 88 | 87 | 88 | 92 | 14 |
| 4, 8, 15, 16, 23, 42 | 18 | 15.5 | none | 38 |
| 7, 7, 7, 7 | 7 | 7 | 7 | 0 |
| 30, 32, 35, 38, 300 | 87 | 35 | none | 270 |
| 1, 2, 2, 3, 3, 4 | 2.5 | 2.5 | 2, 3 | 3 |
Special cases and common mistakes
- One outlier moves the mean, not the median. For 30, 32, 35, 38, 300 the mean is 87 but the median is 35. That is why home prices and household income are usually reported as medians.
- Use a weighted average when items count differently. Course grades with category weights, or the average price paid across purchases of different sizes, both need weights.
- Weights do not have to add up to 100. The calculator divides by the total weight, so weights of 4, 3.5 and 2.5 give the same 86.05 as 40, 35 and 25.
- A comma always separates numbers. Type 1500, not 1,500, or the calculator reads two values. Dollar amounts work the same: $12.50 is entered as 12.5.
Frequently asked questions
How do I calculate the average of numbers?
Add them up and divide by how many there are. 85 + 92 + 78 + 92 + 88 = 435, and 435 ÷ 5 = 87.
What is the difference between mean, median and mode?
The mean is the arithmetic average, the median is the middle value after sorting, and the mode is the most common value. For 78, 85, 88, 92, 92: mean 87, median 88, mode 92.
How do I find the median with an even number of values?
Sort the values and average the two in the middle. For 4, 8, 15, 16, 23, 42 the median is (15 + 16) ÷ 2 = 15.5.
How do I calculate a weighted average for grades?
Multiply each category score by its weight, add the results, and divide by the total weight. With tests 40%, homework 35% and the final 25%, scores of 92, 85 and 78 give 86.05.
Can there be more than one mode?
Yes. In 1, 2, 2, 3, 3, 4 both 2 and 3 appear twice, so the modes are 2 and 3. If no value repeats, there is no mode.