📈 Statistics Calculator

The calculator splits your input on any run of whitespace, commas or semicolons, then sorts the values. Mean is the arithmetic average: the sum of all values divided by the count, written as x-bar = sum(x) / n. Median is the middle value of the sorted list, or the average of the two middle values when n is even. Mode is the value that occurs most often, and the tool reports every value tied for the top frequency rather than picking one arbitrarily.

Spread is reported using the sample formulas. Sample variance is s squared = sum of (x - x-bar) squared, divided by (n - 1), and sample standard deviation is the square root of that. The (n - 1) divisor, known as Bessel's correction, keeps the estimate unbiased when your numbers are a sample drawn from a larger population.

Quartiles use linear interpolation at position p x (n - 1) in the sorted list, the same method as the spreadsheet function PERCENTILE.INC and the default in NumPy. The interquartile range is simply Q3 minus Q1, and range is maximum minus minimum.

Enter 4, 8, 15, 16, 23, 42. The count is 6 and the sum is 108, so the mean is 108 / 6 = 18. Sorted, the list is already 4, 8, 15, 16, 23, 42, and with an even count the median is the average of the third and fourth values: (15 + 16) / 2 = 15.5. Range is 42 - 4 = 38.

For the quartiles, Q1 sits at position 0.25 x (6 - 1) = 1.25 in the zero-indexed sorted list, which is a quarter of the way from 8 to 15: 8 + 0.25 x 7 = 9.75. Q3 sits at 0.75 x 5 = 3.75, three quarters of the way from 16 to 23: 16 + 0.75 x 7 = 21.25. The interquartile range is 21.25 - 9.75 = 11.5.

For variance, the squared deviations from the mean of 18 are 196, 100, 9, 4, 25 and 576, summing to 910. Sample variance is 910 / 5 = 182, and sample standard deviation is the square root of 182, about 13.49. No value repeats, so there is no mode.

Compare the mean and the median before you trust either. In the example above the mean of 18 is higher than the median of 15.5 because the value 42 pulls it upward; that gap is the signature of a right-skewed data set, and the positive skewness figure confirms it. When the two differ noticeably, the median usually describes the typical value better.

Use the interquartile range to test for outliers. The standard fences are Q1 - 1.5 x IQR and Q3 + 1.5 x IQR, which here give -7.5 and 38.5. The value 42 falls outside the upper fence, so it qualifies as an outlier by that convention and is worth investigating before you report the mean.

The most frequent mistake is mixing up sample and population statistics. This tool divides by (n - 1), which is correct when your numbers are a sample. If your list is the entire population, multiply the variance by (n - 1) / n to convert it. Also check for a mode of none: with continuous measurements, no value repeating is normal and does not signal a problem.