Statistics Calculator
Paste a list of numbers to get every common descriptive statistic at once, from the mean and median to quartiles, standard deviation and outliers.
- Free
- No sign-up
- Private
Paste or type numbers separated by commas, spaces or new lines (e.g. a column copied from a spreadsheet).
- Count (n)
- 10
- Sum
- 180
- Mean
- 18
- Median
- 15
- Mode
- 15
- Minimum
- 11
- Maximum
- 40
- Range
- 29
- Q1 (25th percentile)
- 14
- Q3 (75th percentile)
- 19
- Interquartile range
- 5
- Sample variance (sยฒ)
- 69.111111
- Sample standard deviation (s)
- 8.313309
- Population variance (ฯยฒ)
- 62.2
- Population standard deviation (ฯ)
- 7.886698
- Standard error of the mean
- 2.628899
- Coefficient of variation
- 43.81%
- Skewness
- 2.4106
- Geometric mean
- 16.800728
- Outliers (1.5 ร IQR rule)
- 40
How the mean was calculated
- Add up all 10 numbers: 12 + 15 + 11 + 18 + 15 + 21 + 14 + 15 + 19 + 40 = 180.
- Divide the sum by how many numbers there are: 180 รท 10 = 18.
How the median was found
- Sort the numbers from smallest to largest: 11, 12, 14, 15, 15, 15, 18, 19, 21, 40.
- There are 10 numbers (even), so average the two middle values (the 5th and 6th): (15 + 15) รท 2 = 15.
How the variance and standard deviation were calculated
- Find the mean: 18.
- Subtract the mean from each value and square the result, then add those squares: ฮฃ(x โ mean)ยฒ = 622.
- Population variance ฯยฒ = 622 รท 10 = 62.2; population standard deviation ฯ = โ62.2 = 7.886698.
- Sample variance sยฒ = 622 รท (10 โ 1) = 69.111111; sample standard deviation s = โ69.111111 = 8.313309.
What this statistics calculator gives you
Paste a list of numbers and this statistics calculator returns the descriptive statistics most courses and reports ask for in one go: count, sum, mean, median, mode, range, quartiles, interquartile range, variance, standard deviation (both sample and population), standard error, coefficient of variation, skewness, geometric mean and any outliers. The working for the mean, median and variance is shown below the results so you can check each step.
Worked example
Take 12, 15, 11, 18, 15, 21, 14, 15, 19, 40. The sum is 180 and there are 10 values, so the mean is 18. Sorted, the middle two values are 15 and 15, so the median is 15, and 15 is also the mode because it appears three times. The mean is pulled above the median by the 40, which is the clue that the data is right-skewed. The quartiles are Q1 = 14 and Q3 = 19, so the IQR is 5; the upper fence is 19 + 1.5 ร 5 = 26.5, which flags 40 as an outlier.
Mean, median or mode?
The mean uses every value, so it is the best summary for symmetric data but is dragged around by extreme values. The median is the middle value and barely moves when an outlier appears, which is why incomes and house prices are reported as medians. The mode is the most common value and the only one that works for categories. When the mean and median differ a lot, the data is skewed, and the skewness value tells you which way: positive means a long tail to the right.
Sample or population?
Both versions of variance and standard deviation are shown. Use the sample versions (dividing by n โ 1) when your numbers are a subset of a larger group, which is the usual case. Use the population versions (dividing by N) only when you have every member of the group. The dedicated standard deviation calculator shows the full deviation table and z-scores.
Quartiles and outliers
Quartiles here follow Tukey's method: Q1 is the median of the lower half and Q3 the median of the upper half, leaving out the middle value when the count is odd. Excel's QUARTILE.INC and some textbooks interpolate instead, so Q1 and Q3 can differ slightly from a spreadsheet, especially for small lists. An outlier is any value more than 1.5 ร IQR below Q1 or above Q3. A flagged value is not necessarily an error, but it deserves a second look before you rely on the mean. For quick averages, see the mean, median, mode calculator.
Frequently asked questions
What does a statistics calculator calculate?
Descriptive statistics for a list of numbers: count, sum, mean, median, mode, range, quartiles, interquartile range, variance, standard deviation, standard error, skewness and outliers.
What is the difference between sample and population standard deviation?
The sample version divides by n โ 1 and is used when your numbers are a subset of a larger group; the population version divides by N and is used when you have every member of the group.
How are outliers detected?
A value is flagged as an outlier if it is below Q1 โ 1.5 ร IQR or above Q3 + 1.5 ร IQR, where IQR = Q3 โ Q1. This is Tukey's rule, the one used for box plots.
How are the quartiles calculated?
Q2 is the median; Q1 is the median of the lower half and Q3 the median of the upper half, leaving out the middle value when the count is odd. Excel's QUARTILE.INC interpolates, so it can differ slightly.
What does skewness tell you?
Which way the data leans. A positive value means a longer tail to the right (mean above median); a negative value means a longer tail to the left; near zero means roughly symmetric.
How many numbers can I enter?
Up to 10,000, separated by commas, spaces or new lines, so you can paste a column straight from a spreadsheet.