Statistics Calculator

Paste a list of numbers and this gives you the usual summary: count, sum, mean, median, mode, range, quartiles, interquartile range, variance and standard deviation. The spread measures come in both population and sample versions, so you can use whichever your course or analysis needs without redoing anything.

How to use it

1. Paste or type your numbers, separated by commas, spaces or new lines.
2. Read the summary values.
3. Check the sorted list to be sure the data was read correctly.
4. Copy the figures you need.

When it helps

• Analysing survey results or test scores.
• Statistics homework.
• Getting a quick description of a data set.
• Spotting outliers with the quartiles.

Good to know

• Use the sample standard deviation when your numbers are a sample from a larger group; it divides by one less than the count.
• A mode is listed only when a value actually repeats.
• Quartiles use the median-of-halves method, and other textbooks sometimes use slightly different ones.

What the measures tell you

The mean is the average, which is pulled by extreme values. The median is the middle value, which resists outliers. The mode is the most common value. The range, from smallest to largest, shows spread, and the standard deviation shows how far values typically sit from the mean.

Quartiles split the sorted data into four parts. The interquartile range, Q3 minus Q1, is the spread of the middle half and is a robust measure of variation.

Worked example: exam scores

Scores of 4, 8, 15, 16, 23, 42 and 15 give a mean of 17.57, a median of 15, a mode of 15, a range of 38 and a sample standard deviation of about 12.4. The mean is higher than the median because the 42 pulls it up, a hint that the data is skewed.

Comparing the mean and median is a quick check for skew.

Sample or population

If your numbers are every member of the group you care about, such as all students in one class, use the population measures. If they're a sample from a larger group, such as a survey of 100 voters, use the sample ones, which divide by n minus 1 to avoid understating the spread.

With large data sets the two are very close, and the difference matters most for small samples.

Spotting outliers

A common rule treats values more than 1.5 times the interquartile range below Q1 or above Q3 as outliers. Check any you find: they may be errors, or they may be the most interesting part of the data.

Don't remove them just because they're awkward. Decide with a reason, and note that you did so.

Choosing the right average

The mean suits symmetric data, such as heights. The median suits skewed data, such as incomes or house prices, where a few huge values drag the mean up. The mode suits categories, such as the most popular shoe size.

When reporting results, say which average you used. Choosing the one that flatters your story is a classic way statistics mislead.

Questions