Descriptive statistics

Calculate mean, median, mode, range, and standard deviation from a set of values.

What is this for?

The three measures of central tendency answer subtly different questions. The mean uses every value and is pulled by outliers; the median is the middle value and resists them; the mode is the most frequent value and is the only one meaningful for nominal data. Which to report depends on the distribution and the level of measurement.

How to use it

Paste or type your values into the box. Commas, spaces, tabs, and line breaks all work as separators, so a copied spreadsheet column can be pasted directly.
Choose the sample standard deviation unless your data genuinely represent an entire population.
Compare the mean and median — a large gap between them is the quickest signal of skew or outliers.

Worked example

Calculate the descriptive statistics for the data set 12, 15, 15, 18, 22, 24, 31.

Answer: n = 7, sum = 137, mean = 19.57, median = 18 (the fourth of seven ordered values), mode = 15 (appears twice), range = 19, sample SD = 6.55.

Clinical pearls & pitfalls

Report the median and interquartile range for skewed data — length of stay, cost, time to event — and the mean with standard deviation for roughly symmetric data.
The mode is the only measure of central tendency that works for nominal data such as the most commonly prescribed agent in a class.
A data set can have no mode (every value unique), one mode, or several. Reporting "the mode" without checking is a common error.
The sample standard deviation divides by n − 1 rather than n. This Bessel correction matters at small sample sizes and is the default in almost all statistical software.
The coefficient of variation expresses spread relative to the mean, which allows comparison of variability between measures on entirely different scales.

Assumptions & limitations

Descriptive only. No inferential statistics, hypothesis tests, or confidence intervals are produced.
Univariate. Correlation, regression, and group comparison require dedicated methods.
Assumes the values entered are the complete data set. Missing data are not detected or handled.
Quartiles are calculated by linear interpolation. Different conventions exist and can give slightly different values for small samples.

References

Altman DG, Bland JM. Statistics notes: presentation of numerical data. BMJ. 1996;312(7030):572.
Lang TA, Altman DG. Basic statistical reporting for articles published in biomedical journals: the SAMPL guidelines. Int J Nurs Stud. 2015;52(1):5-9.