justyourcalculatorMean, Median, Mode, Range Calculator
The four classic averages and spreads, worked out step by step.
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Mean, Median, Mode, Range Calculator
Mean, median, mode and range with steps
Separate values with commas, spaces or new lines.
Mean
18
Median 18.5 · Mode 23 · Range 13
- Mean (average)
- 18
- Median
- 18.5
- Mode
- 23 (3 times)
- Range
- 13
- Minimum
- 10
- Maximum
- 23
- Count
- 8
- Sum
- 144
- Quartiles Q1, Q3
- 14, 23
- Interquartile range
- 9
- Outliersbeyond 1.5 × IQR
- None
- Geometric mean
- 17.252538
- Root mean square
- 18.654758
Quartiles use the median of each half (the median itself is left out when the count is odd).
How it was calculated
- Sorted: 10, 12, 16, 16, 21, 23, 23, 23
- Mean: sum / count = 144 / 8 = 18
- Median: 8 values (even), so average the middle two, #4 and #5: (16 + 21) / 2 = 18.5
- Mode: 23 appears 3 times, 16 appears 2 times. Most frequent: 23
- Range: largest - smallest = 23 - 10 = 13
| Value | Frequency | Relative | Deviation (x - mean) | (x - mean)² | Frequency × (x - mean)² |
|---|---|---|---|---|---|
| 10 | 1 | 12.5% | -8 | 64 | 64 |
| 12 | 1 | 12.5% | -6 | 36 | 36 |
| 16 | 2 | 25% | -2 | 4 | 8 |
| 21 | 1 | 12.5% | 3 | 9 | 9 |
| 23 | 3 | 37.5% | 5 | 25 | 75 |
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How the mean, median, mode, range calculator works
The mean is the ordinary average: add the numbers and divide by how many there are. The median is the middle value once the numbers are sorted; with an even count it is the average of the two middle values. The mode is the value that appears most often, and a list can have several modes or none. The range is the largest value minus the smallest.
The mean uses every value, so a single very large or small number can pull it a long way. The median ignores extremes, which is why it is used for things like house prices and incomes. Compare the two: if the mean is well above the median, the data has a long upper tail.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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