Statistics Calculator

What this tool is used for

• Getting mean, median and spread for a pasted list of numbers.
• Checking whether a distribution is skewed before choosing a summary statistic.
• Computing quartiles so a box plot's whiskers can be drawn correctly.
• Comparing two datasets on spread rather than average.
• Confirming a figure you calculated another way.

Frequently Asked Questions

When should I use the median instead of the mean?

Whenever the data is skewed or has outliers. Income is the standard example: a handful of very high earners pull the mean well above what a typical person earns, while the median tracks the middle of the distribution.

What is the difference between sample and population variance?

The divisor: population uses n, sample uses n−1 (Bessel's correction). Using n on a sample systematically UNDERSTATES the variance, because the sample mean sits closer to its own data than the true mean does. Almost all real data is a sample.

What does standard deviation actually tell me?

The typical distance from the mean, in the data's own units — unlike variance, which is in squared units. For roughly normal data, about 68% of values fall within one standard deviation and 95% within two.

Can a dataset have more than one mode?

Yes. Two equally frequent peaks make it bimodal, which usually signals two mixed populations — adult heights across both sexes, for instance. A bimodal dataset is one where the mean describes almost nobody.

What is the interquartile range for?

The spread of the middle 50%, from Q1 to Q3. It is robust to outliers where standard deviation is not, which is why box plots use it and why the common outlier test is anything beyond 1.5 × IQR from the quartiles.

Why is n−1 used for a sample?

Because the sample mean is itself estimated from the data, so deviations from it are systematically too small. Dividing by n−1 — Bessel's correction — compensates, giving an unbiased estimate of the population variance.

What does skew tell me?

Which tail is longer, and therefore how far the mean has been pulled from the median. Positive skew — common in incomes and response times — means the mean sits above the median and reports a typical value that is not typical.

Common errors and gotchas

• Quoting the mean for a skewed distribution, where the median describes it far better.
• Confusing the sample and population standard deviation, which differ by the denominator.
• Using a quartile method without saying which, since several conventions give different answers.
• Including outliers without noting them, which can move the mean a long way.
• Reading a statistic as a conclusion rather than a description.