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Statistics Calculator
Paste or type a list of numbers to get every common summary statistic at once: count, sum, mean, median, mode, minimum, maximum and range, sample and population standard deviation and variance, quartiles, the interquartile range and any outliers. A table lists each value’s deviation from the mean, so you can follow how the variance is built.
- Median
- 85
- Mode
- 85
- Count (n)
- 10
- Sum
- 836
- Minimum
- 66
- Maximum
- 95
- Range
- 29
- Sample standard deviation (s)
- 9.0823
- Population standard deviation (σ)
- 8.6163
- Sample variance (s²)
- 82.4889
- Population variance (σ²)
- 74.24
- First quartile (Q1)
- 78
- Third quartile (Q3)
- 90
- Interquartile range (IQR)
- 12
- Outliers (1.5 × IQR rule)
- None
- Standard error of the mean
- 2.8721
- Coefficient of variation
- 10.86%
- Sorted
- 66, 72, 78, 85, 85, 85, 88, 90, 92, 95
Deviations from the mean
| # | Value (x) | x − mean | (x − mean)² |
|---|
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Type or paste your numbers, separated by commas, spaces or new lines.
- Read the mean and the rest of the summary. Quartiles and outliers appear once there are at least four values.
- Use the deviations table to check the variance by hand: add up the squared deviations, then divide by n or by n − 1.
Worked examples
Ten test scores
- Mean (average)
- 83.6
- Median
- 85
- Mode
- 85
- Count (n)
- 10
- Sum
- 836
- Range
- 29
- Sample variance (s²)
- 82.4889
- Population variance (σ²)
- 74.24
- Sample standard deviation (s)
- 9.0823
- Population standard deviation (σ)
- 8.6163
- First quartile (Q1)
- 78
- Third quartile (Q3)
- 90
- Interquartile range (IQR)
- 12
- Outliers (1.5 × IQR rule)
- None
- Standard error of the mean
- 2.8721
- Coefficient of variation
- 10.86%
The textbook set 2, 4, 4, 4, 5, 5, 7, 9
- Mean (average)
- 5
- Median
- 4.5
- Mode
- 4
- Range
- 7
- Population standard deviation (σ)
- 2
- Population variance (σ²)
- 4
- Sample variance (s²)
- 4.5714
- Sample standard deviation (s)
- 2.1381
- First quartile (Q1)
- 4
- Third quartile (Q3)
- 6
- Interquartile range (IQR)
- 2
- Outliers (1.5 × IQR rule)
- None
Ten values with one far from the rest
- Mean (average)
- 19.5
- Median
- 16.5
- Mode
- 15
- First quartile (Q1)
- 15
- Third quartile (Q3)
- 19
- Interquartile range (IQR)
- 4
- Outliers (1.5 × IQR rule)
- 48
Sample or population?
Use the population figures when your list is the entire group you care about, such as every student in one class. Use the sample figures when the list is part of a larger group you want to describe, such as 50 customers out of thousands. Dividing by n − 1 instead of n (Bessel’s correction) stops the sample variance from underestimating the spread of the whole group.
For the ten test scores in the first example, the squared deviations add up to 742.4. Divided by 10 that is a population variance of 74.24 and a standard deviation of 8.62; divided by 9 it is 82.49 and 9.08.
Which average to report
The mean uses every value, so one extreme value pulls it. In the outlier example the mean is 19.5 but the median is 16.5, because of the 48. For skewed data such as incomes or house prices, the median is usually the better summary. The mode is most useful for repeated values, such as the most common shoe size.
How the quartiles are worked out
Q1 and Q3 are the medians of the lower and upper halves of the sorted data, leaving the middle value out when the count is odd. This is the method used by TI-83 and TI-84 calculators and most US textbooks. Spreadsheet functions such as Excel’s QUARTILE.INC interpolate instead, and can give slightly different values on small data sets.
Questions people ask
How do I find the mean, median and mode?
Mean: add the values and divide by how many there are. Median: sort them and take the middle one, or the average of the middle two. Mode: the value that appears most often. For 72, 85, 90, 66, 85, 78, 92, 88, 95, 85 they are 83.6, 85 and 85.
What is the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9?
2 as a population standard deviation, or about 2.138 as a sample standard deviation. The mean is 5 and the squared deviations add up to 32; 32 ÷ 8 = 4, and √4 = 2.
What counts as an outlier?
Under the common 1.5 × IQR rule, any value more than 1.5 interquartile ranges below Q1 or above Q3. In 12, 14, 15, 15, 16, 17, 18, 19, 21, 48 the upper fence is 19 + 1.5 × 4 = 25, so 48 is an outlier.
Why do my calculator and Excel give different standard deviations?
One is probably using the sample formula (Excel’s STDEV.S) and the other the population formula (STDEV.P). This calculator shows both.