Statistics calculator with steps

What this page covers

• Measures of center: mean, median and mode.
• Measures of spread: range, variance and standard deviation, for a sample (divide by $n - 1$) or a whole population (divide by $n$).
• Standard scores ($z$-scores) for a value in a data set.
• Not covered here: probability questions (use Probability calculator) and comparing several groups with ANOVA (use ANOVA calculator).

How to enter the problem

• Type the data separated by commas, then say what you need, such as sample standard deviation.
• Scan it. Fit the one problem in the frame.
• Choose a photo. Several problems in one photo are solved as a list.
• Then tap Solve.

Worked examples

Common mistakes

• Dividing by $n$ when the data are a sample. For the runnable example that gives $\sqrt{\frac{64}{5}} \approx 3.58$ instead of 4.
• Finding the median without sorting first. In 12, 5, 9, 20, 7, 15 as written, the middle pair is 9 and 20, which gives the wrong median.
• Forgetting to square the deviations. The plain deviations from the mean add to 0, so they say nothing about spread.
• Using the population standard deviation in a z-score when the data are a sample, or the reverse.

Checks, assumptions and limits

• Check that the deviations add to 0. For the runnable example the mean is 8, and $-5 - 1 - 1 + 1 + 6 = 0$.
• A standard deviation is never negative, and it is 0 only when every value is the same.
• Sample formulas assume the data come from a larger group; population formulas assume the data include every member of the group.
• HexMath can make mistakes. Double check important steps.

Related tasks

• Average calculator with steps
• Find the median of a data set
• Probability of an event
• All statistics and probability tasks
• All math tasks