Statistics Calculator

Mean, median, mode, standard deviation and quartiles with steps.

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Statistics Calculator

Mean, median, mode, spread and quartiles

NumbersSeparate with commas, spaces or new lines.

Variance and SD for

Mean5

Median4.5

Mode4appears 3 times

Population standard deviation2

Population variance4

Count8sum 40

Range72 to 9

Q1 · Q34 · 6IQR 2

How often each value appears

How it works

The mean is the average, the median is the middle value and the mode is the most common value. Standard deviation tells you how spread out the numbers are around the mean; quartiles split the sorted data into four equal parts.

Sort the 8 values: 2, 4, 4, 4, 5, 5, 7, 9.
Mean = sum ÷ count = 40 ÷ 8 = 5.
Median: n = 8 is even, so average the two middle values (numbers 4 and 5): (4 + 5) ÷ 2 = 4.5.
Mode: 4 appears 3 times.
Range = largest − smallest = 9 − 2 = 7.
Q1 = median of the lower half (2, 4, 4, 4) = 4.
Q3 = median of the upper half (5, 5, 7, 9) = 6. IQR = Q3 − Q1 = 6 − 4 = 2.
Squared deviations: add up (x − mean)² over all values. Σ(x − 5)² = 32.
Population variance = Σ(x − mean)² ÷ n = 32 ÷ 8 = 4.
Standard deviation = √variance = √4 = 2.

Use population when your list is every value there is, and sample when it is a part taken from a bigger group.
With a frequency table, enter each different value once with how many times it occurs.
A big gap between mean and median often means a few extreme values.

Two-pass computation: the mean first, then the sum of squared deviations. Population variance divides by n, sample variance by n − 1 (Bessel's correction). Quartiles are the medians of the lower and upper halves of the sorted data, leaving out the middle value when n is odd.

Preparing tool

How to use Statistics Calculator

Paste your numbers, or switch to a frequency table and enter each value with its count.
Choose population or sample for variance and standard deviation.
Read the results and the working, then copy them or share a link.

Read the detailed guide →

What are the limits of Statistics Calculator?

Quartiles use the classroom method (median of each half, middle value left out for an odd count); spreadsheets may differ slightly. Up to 100,000 values. Nothing you enter leaves your device.