Statistics calculator

Descriptive statistics summarise a dataset in a few numbers: where its centre is and how spread out it is. This calculator computes the most common measures from a list of numbers, such as test scores, response times, sales figures or measurements.

How to use it

1. Paste or type numbers separated by commas, spaces or new lines.
2. Read the count, sum, mean, median, mode, range, variance, standard deviation and quartiles.

Worked example

Data: 2, 4, 4, 4, 5, 5, 7, 9 (8 values, sum 40).

• Mean: 40 / 8 = 5
• Median: average of the 4th and 5th values, (4 + 5) / 2 = 4.5
• Mode: 4, which appears three times
• Range: 9 - 2 = 7
• Population variance: sum of squared deviations (32) / 8 = 4, so population standard deviation = 2
• Sample variance: 32 / 7 = 4.571, so sample standard deviation = 2.138

Sample vs. population

Use the population formula (divide by n) when your data includes every member of the group you care about. Use the sample formula (divide by n - 1, Bessel's correction) when the data is a sample used to estimate a larger population, which is the usual case in research and analytics. Spreadsheets reflect this: STDEV.P vs STDEV.S.

Mean or median?

The mean is sensitive to outliers. Salaries 30k, 35k, 40k and 400k have a mean of 126k but a median of 37.5k. For skewed data such as income, house prices and response times, the median better describes a typical value.

Quartiles

Q1, Q2 (median) and Q3 split sorted data into four parts. The interquartile range (Q3 - Q1) is a robust measure of spread. Different software uses slightly different quartile methods, so small differences are normal.