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Statistics Calculator
Mean, median, standard deviation and more
Separate values with commas, spaces or new lines.
Mean (average)
81.066667
15 values, sum 1,216
Center
- Mean
- 81.066667
- Median
- 85
- Mode
- 85 (3 times)
- Geometric meanpositive values only
- 80.465142
- Harmonic meanpositive values only
- 79.827363
Spread
- Standard deviation (sample)
- 9.910072
- Standard deviation (population)
- 9.574039
- Variance (sample)
- 98.209524
- Variance (population)
- 91.662222
- Range61 to 95
- 34
- Quartiles Q1, Q3
- 72, 88
- Interquartile range
- 16
- Mean absolute deviation
- 8.053333
- Standard error of the mean
- 2.55877
- Coefficient of variation
- 12.225%
Shape and totals
- Count
- 15
- Sum
- 1,216
- Sum of squares
- 99,952
- Minimum
- 61
- Maximum
- 95
- Skewnesssample, needs 3+ values
- -0.6929
- Excess kurtosissample, needs 4+ values
- -0.3721
- Outliersbeyond 1.5 × IQR
- None
Quartiles use the median of each half (the median itself is left out when the count is odd). Skewness and kurtosis are the sample-adjusted versions used by Excel.
- Count
| Value | Frequency | Relative | Deviation (x - mean) | (x - mean)² | Frequency × (x - mean)² |
|---|---|---|---|---|---|
| 61 | 1 | 6.67% | -20.066667 | 402.671111 | 402.671111 |
| 66 | 1 | 6.67% | -15.066667 | 227.004444 | 227.004444 |
| 70 | 1 | 6.67% | -11.066667 | 122.471111 | 122.471111 |
| 72 | 1 | 6.67% | -9.066667 | 82.204444 | 82.204444 |
| 78 | 1 | 6.67% | -3.066667 | 9.404444 | 9.404444 |
| 79 | 1 | 6.67% | -2.066667 | 4.271111 | 4.271111 |
| 83 | 1 | 6.67% | 1.933333 | 3.737778 | 3.737778 |
| 85 | 3 | 20% | 3.933333 | 15.471111 | 46.413333 |
| 87 | 1 | 6.67% | 5.933333 | 35.204444 | 35.204444 |
| 88 | 1 | 6.67% | 6.933333 | 48.071111 | 48.071111 |
| 90 | 1 | 6.67% | 8.933333 | 79.804444 | 79.804444 |
| 92 | 1 | 6.67% | 10.933333 | 119.537778 | 119.537778 |
| 95 | 1 | 6.67% | 13.933333 | 194.137778 | 194.137778 |
| Rank | Value |
|---|---|
| 1 | 61 |
| 2 | 66 |
| 3 | 70 |
| 4 | 72 |
| 5 | 78 |
| 6 | 79 |
| 7 | 83 |
| 8 | 85 |
| 9 | 85 |
| 10 | 85 |
| 11 | 87 |
| 12 | 88 |
| 13 | 90 |
| 14 | 92 |
| 15 | 95 |
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How the statistics calculator works
Descriptive statistics summarize a data set. The mean is the sum divided by the count; the median is the middle value when sorted; the mode is the most frequent value. The range, quartiles and interquartile range (IQR = Q3 − Q1) describe how spread out the data is.
Standard deviation measures the typical distance from the mean. Use the sample version (divide by n − 1) when your data is a sample of a larger group, and the population version (divide by n) when it is the whole group. Variance is the standard deviation squared.
Skewness shows whether the data leans to one side (positive means a long right tail), and excess kurtosis compares the tails to a normal distribution (0 is normal). Values more than 1.5 × IQR beyond the quartiles are flagged as outliers.
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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