MihsabaArithmetic, weighted or harmonic mean?
The arithmetic mean divides the total by the number of observations. For values with unequal weights or for some rates, a different method is needed.
Use this calculator for: Calculating arithmetic mean, median, sum and range for a list of equally weighted numbers.
- Find a weighted average — Use when grades or observations carry different weights or credit hours.
- Measure standard deviation — Measure how spread out the data are around their average.
- Calculate a harmonic mean — Useful for certain rates, such as average speed across equal-distance legs.
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Mean vs Median: When to Use Each (With Examples)
How to use
This average calculator analyzes a list of numbers and reports more than the arithmetic mean: mean, median, sum, count, minimum, maximum and range. The mean describes the overall center, while the median can be more representative when extreme values pull the mean up or down.
- Enter one or more numbers separated by commas, semicolons or new lines.
- Make sure each entry is a separate number, especially when using decimals.
- Review the mean, median, sum and count, then compare minimum, maximum and range.
- Use the sorted values to understand the median and spread at a glance.
How it is calculated
Example
Example: for 10, 20, 30 and 100, the sum is 160 and the mean is 40, while the median is (20 + 30) ÷ 2 = 25. The minimum is 10, maximum 100 and range 90. The gap between mean 40 and median 25 shows how the value 100 pulls the mean upward.
Important notes
Every value has equal weight here. If some values matter more than others, such as courses with different credit hours, use a weighted average. Range only uses the minimum and maximum and does not describe the full distribution of the data.
Worked examples and interpreting results
For the list 8, 10, 12, the mean divides the sum by the count. The median identifies the middle value after sorting; the range measures the gap between the largest and smallest values.
| Case | Calculation | Result |
|---|---|---|
| Mean | (8 + 10 + 12) ÷ 3 | 10 |
| Median | 8 < 10 < 12 | 10 |
| Range | 12 − 8 | 4 |
How to check the result
Use a weighted average when values represent groups of different sizes or carry different importance. For grades weighted 40% and 60%, open the weighted-average calculator instead of treating both grades equally.
How outliers and weights change an average
Worked case
For 10, 11, 12, 13 and 54, the arithmetic mean is 20 but the median is only 12. The larger observation pulls the mean above four of the five values.
Compare another scenario
Grades 80 and 90 with respective weights 1 and 3 yield a weighted mean of 87.5; treating them as equally weighted gives 85.
How to interpret the result
Use the median for strongly skewed observations and a weighted mean when grades or categories carry different credits. Always validate the sum and count.
Calculate mean versus median
The arithmetic mean is the sum divided by the number of entries. The median is the central number after sorting and may be more representative with outliers.
- Mean of 7, 9, 14: (7 + 9 + 14) ÷ 3 = 10
- Mean of 3, 3, 20: (3 + 3 + 20) ÷ 3 = ≈ 8.67
- Median of 3, 3, 20: 3 ≤ 3 ≤ 20 = 3
Important note
Use a weighted mean rather than a simple average when observations have unequal importance, such as grades with different credit hours.
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Frequently asked questions
How do I calculate the arithmetic mean?
Add all values and divide by the number of values.
How is the median calculated?
Sort the values. With an odd count, take the middle value; with an even count, average the two middle values.
What is the difference between mean and median?
The mean uses every value and is more sensitive to outliers, while the median depends on the ordered position.
What is range?
Range = maximum − minimum.
Can I enter negative and decimal numbers?
Yes, as long as each entry is a valid number and values are separated correctly.
When should I use a weighted average?
Use it when observations do not have equal importance or weight.