Statistics Calculator
Paste or type a list of numbers and get every common descriptive statistic at once, with a histogram, a box plot and a frequency table that update live.
Separate numbers with commas, spaces or new lines. You can paste a column straight from a spreadsheet.
Descriptive statistics
Quartiles use the median-of-halves method (the median is left out of both halves when the count is odd), the same method most textbooks and TI calculators use. Outliers are values below Q1 − 1.5×IQR (6.5) or above Q3 + 1.5×IQR (26.5). Skewness is the adjusted sample skewness. Geometric and harmonic means need every value to be positive.
Histogram
Box plot
Box spans Q1 to Q3, the purple line is the median, whiskers reach the furthest points inside the 1.5×IQR fences, and orange dots are outliers.
Frequency table
| Value | Count | Percent |
|---|---|---|
| 11 | 1 | 7.1% |
| 12 | 1 | 7.1% |
| 13 | 1 | 7.1% |
| 14 | 1 | 7.1% |
| 15 | 3 | 21.4% |
| 16 | 1 | 7.1% |
| 17 | 1 | 7.1% |
| 18 | 1 | 7.1% |
| 19 | 1 | 7.1% |
| 21 | 1 | 7.1% |
| 22 | 1 | 7.1% |
| 45 | 1 | 7.1% |
The mean is the sum divided by the count, the median is the middle value of the sorted data, and the mode is the value that appears most often (there can be several, or none if every value appears once). The range, quartiles and interquartile range (IQR) describe how spread out the data is.
Population variance divides the sum of squared deviations by n and is right when your data is the whole group you care about. Sample variance divides by n − 1 and is the better estimate when your data is a sample from a larger group. The standard deviation is the square root of each, and the standard error is the sample standard deviation divided by √n.
Outliers are flagged with the 1.5×IQR rule: anything below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. The histogram uses Sturges' rule to choose the number of bins, which works well for small and medium-sized data sets.
Frequently asked questions
Should I use the sample or the population standard deviation?
Use the population version when your numbers cover everyone or everything you are studying, such as the test scores of an entire class. Use the sample version when the numbers are a sample drawn from a bigger group and you want to estimate that group's spread. When in doubt, the sample standard deviation is the usual choice.
Why are my quartiles different from Excel?
There are several accepted ways to compute quartiles. This calculator uses the median-of-halves method taught in most textbooks and used by TI calculators. Excel's QUARTILE.INC interpolates between values instead, so the two can differ slightly for small data sets.
What counts as an outlier?
A value is flagged as an outlier if it lies more than 1.5 times the interquartile range below the first quartile or above the third quartile. These points are drawn as orange dots on the box plot.
Why is the geometric mean missing?
The geometric and harmonic means are only defined here when every value is positive, because they use logarithms and reciprocals. If your data contains zero or a negative number, they are shown as a dash.
