Descriptive Statistics Calculator — full data summary

How it works

Descriptive statistics reduce a whole data set to a few summary numbers, grouped into measures of location (where the data sits) and scale (how spread out it is):

• Count & sum — how many values there are and their total.
• Location (MathWorld): the mean (sum ÷ count), the median (the middle of the ordered data), and the mode (the most frequent value).
• Scale (NIST e-Handbook): the minimum and maximum, the range (maximum − minimum), and the variance and standard deviation, computed with the sample divisor n − 1.

Together these answer the everyday questions about a data set — what is typical, and how much do the values vary. Enter your numbers separated by commas, spaces or new lines.

Worked example

For 2, 4, 4, 4, 5, 5, 7, 9 (8 values, sum 40): the mean is 5, the median is 4.5, and the mode is 4. The smallest value is 2 and the largest is 9, so the range is 7. The sample variance is about 4.5714 and the sample standard deviation about 2.1381.

Frequently asked questions

What are descriptive statistics?

They are summary numbers that describe a data set's size, center and spread — count, sum, mean, median, mode, minimum, maximum, range, variance and standard deviation — without drawing conclusions beyond the data itself.

What is the difference between measures of location and scale?

Measures of location (mean, median, mode) describe where the center of the data is; measures of scale (range, variance, standard deviation) describe how spread out the values are around that center.

Does this use sample or population standard deviation?

It reports the **sample** variance and standard deviation, which divide by n − 1 — the usual choice when your numbers are a sample of a larger population. Use the dedicated standard-deviation calculator if you need the population form.

What does the mode show if nothing repeats?

A dash. When every value occurs the same number of times there is no single most-frequent value, so the mode is undefined for that data set.

How many numbers can I enter?

Enter as many as you like, separated by commas, spaces or new lines. The calculator ignores any token that is not a number, so pasting a column of data works.

How is this different from the individual calculators?

It bundles the mean/median/mode, range and standard-deviation results into one summary. Use it for a quick overview, or the focused calculators when you need just one measure explained in depth.