Math & Number Tools Calculator
Statistics Calculator
Use this free Statistics Calculator to calculate statistics with a cleaner layout, instant results, formulas, examples, and helpful interpretation notes.
Explore your data set
Separate values with commas, spaces, semicolons or new lines. For decimal commas, put each value on a new line or separate values with semicolons. Up to 500 values.
Your statistics
Data distribution
The chart shows your values and marks the mean and median. For larger data sets it becomes a histogram.
A large gap can signal skew or influential values. Compare the two, then inspect the chart and raw data before drawing conclusions.
Quartiles and possible outliers
The box spans Q1 to Q3. Whiskers end at the most extreme non-outlier values; points beyond 1.5 × IQR are flagged for review.
Quartiles use the median-of-halves method; for an odd count, the overall median is excluded from each half.
How each result was calculated
Sorted values
Sample variance and sample standard deviation require at least two values.
Value frequencies
| Value | Frequency | Share |
|---|
Your statistics: A ↔ B
| Value | A | B | B − A |
|---|
Data distribution: A / B
How each result was calculated
Choose population when the data includes every member of the group of interest. Choose sample when the data is a subset used to estimate a larger group; sample variance divides by n − 1.
Quartiles use the median-of-halves method; for an odd count, the overall median is excluded from each half.
Sample (n − 1)
Mean: 112 ÷ 6 = 18.6667
Median: (15 + 18) ÷ 2 = 16.5
Variance: Σ(x − x̄)² ÷ (n − 1) = 42.2667
Standard deviation: √42.2667 = 6.5013
With one value, n − 1 is zero, so sample variance and sample standard deviation are undefined.
Standard deviation FAQ
Should I choose population or sample?
Choose population when the data includes every member of the group of interest. Choose sample when the data is a subset used to estimate a larger group; sample variance divides by n − 1.
Does a value outside two standard deviations mean an error?
No. It is only a large standardized deviation in this data set. Investigate the value and the distribution before interpreting it.
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