THE NUMORIX GUIDE
How to use the Statistics Calculator
Last reviewed September 14, 2026
What this calculator does
Parse the comma-separated data, sort a copy for the median, compute mean = sum(x) / n, range = max - min, population variance = sum((x - mean)^2) / n, and standard deviation = sqrt(variance).
Formula and method
Parse the comma-separated data, sort a copy for the median, compute mean = sum(x) / n, range = max - min, population variance = sum((x - mean)^2) / n, and standard deviation = sqrt(variance). Frequencies determine the mode.
Variables and inputs
Data defaults to 4, 8, 15, 16, 23, 42 and is a comma-separated list of numeric observations. The current engine treats the list as a population for variance and standard deviation.
Worked example
For 4, 8, 15, 16, 23, 42: sum = 108 and n = 6, so mean = 18; median = (15 + 16) / 2 = 15.5; range = 42 - 4 = 38; population variance = 910 / 6 = 151.67; population standard deviation = 12.32.
How to interpret the result
Mean and median describe center, range and standard deviation describe spread, and mode describes repeated values. They answer different questions about the same list.
Common mistakes to avoid
Do not confuse population standard deviation with sample standard deviation. Check that numbers were not accidentally omitted by malformed comma-separated input.
Assumptions and limitations
There is no sample-variance option in this engine. When every value is unique, the implementation's mode field is not meaningful and can display the first value rather than saying no mode.
Practical use and checks
Use the Statistics Calculator for a compact description of a numeric list before making a comparison. Enter comma-separated observations such as 2, 4, 4, 6. The result should show count 4, mean 4, median 4, mode 4, minimum 2, maximum 6, range 4, population variance 2, and population standard deviation about 1.41. That example is useful because the repeated 4 makes the mode easy to verify and the range check is simply 6 minus 2. Reordering the same values should not change the summary, although the calculator sorts a copy internally for median and extrema. Use mean and standard deviation when the distribution and purpose support them, but inspect the raw list when an outlier or skew is possible. The mode can be a list when several values tie, and a list with all unique values can make a mode label less meaningful than the other measures. This engine parses numeric prefixes from comma-separated text and silently discards entries that parse as invalid, so a typo can change count without an obvious warning. It reports population-style variance using division by n, not sample variance using n-1. Empty input returns zeros, which is a display fallback rather than evidence that the underlying population has no variation.