Descriptive Statistics Calculator – Mean, Median, Mode, Range & Quartiles

Descriptive statistics summarise a whole data set with a handful of numbers: measures of centre (mean, median, mode), measures of spread (range, variance, standard deviation, interquartile range) and position (quartiles, percentiles). Worked example with 2, 4, 4, 4, 5, 5, 7, 9: the mean is 40 ÷ 8 = 5; sorting gives 2, 4, 4, 4, 5, 5, 7, 9 so the median is (4 + 5) ÷ 2 = 4.5; the mode is 4 (three occurrences); the range is 9 − 2 = 7; the first quartile Q1 = 4 and third quartile Q3 = 6.5, giving an interquartile range (IQR) of 2.5; and the population standard deviation is σ = 2. The IQR is robust to outliers where the range is not — replace the 9 with 90 and the range explodes to 88 while the IQR barely moves. Reading the mean alongside the median also flags skew: a mean well above the median indicates a long right tail.

1. 1

   Paste your data set

   Enter numbers separated by commas or spaces, e.g. 2, 4, 4, 4, 5, 5, 7, 9.

2. 2

   The calculator sorts and counts

   Values are ordered (n = 8) so that median and quartiles can be read off directly.

3. 3

   Read every statistic at once

   Mean 5, median 4.5, mode 4, range 7, Q1 4, Q3 6.5, IQR 2.5, population σ 2 and variance 4.

• 1

  Descriptive statistics describe data without making inferences about a population

• 2

  Always examine multiple statistics together for a complete picture

• 3

  Quartiles divide data into four equal parts: 25%, 50%, 75%

• 4

  The five-number summary (min, Q1, median, Q3, max) is basis for box plots

• 5

  Use descriptive statistics to check data quality before analysis

• Relying on a single statistic instead of examining multiple measures

• Not visualizing data alongside numerical summaries

• Calculating statistics on non-numerical or categorical data inappropriately

• Ignoring sample size when interpreting results

• Confusing descriptive and inferential statistics