📊 Descriptive Statistics Calculator
Paste your numbers to get a full statistical summary — mean, median, mode, quartiles, standard deviation and more.
Count (n)
8
Sum
40
Mean
5
Median
4.5
Mode
4
Min
2
Max
9
Range
7
Q1 (25%)
4
Q3 (75%)
5.5
IQR
1.5
Std dev (sample)
2.138
Std dev (pop.)
2
Variance (sample)
4.571
Variance (pop.)
4
Sample statistics (dividing by n − 1) estimate a population from a sample and are the usual default; population statistics (dividing by n) apply when your data is the whole population. Quartiles use linear interpolation (the inclusive method, matching Excel\'s QUARTILE.INC). Mode shows every most-frequent value, or "none" when all values are unique. 🔒 In your browser.
How the descriptive statistics calculator works
Enter a list of numbers and the tool computes the whole descriptive summary: the measures of centre (mean, median, mode), spread (range, interquartile range, variance and standard deviation) and the five-number summary (min, Q1, median, Q3, max). It shows both sample statistics (dividing by n − 1, the usual estimate from a sample) and population statistics (dividing by n, when your data is the entire population). Quartiles use linear interpolation, matching Excel's QUARTILE.INC.
Use sample statistics when your data is a sample drawn from a larger group you want to describe — that's the default in most research. Use population statistics only when you truly have every member of the group. The mode shows every most-frequent value (data can be multi-modal) or "none" when all values are distinct.
Frequently asked questions
What are descriptive statistics?
Numbers that summarise a data set: measures of centre (mean, median, mode), of spread (range, variance, standard deviation, IQR) and position (quartiles, min, max). They describe the data at hand, unlike inferential statistics which generalise to a population.
What is the difference between sample and population standard deviation?
Sample standard deviation divides the summed squared deviations by n − 1 (Bessel's correction) to estimate a population from a sample; population standard deviation divides by n and is used when you have the entire population. The sample version is the usual default.
How are quartiles calculated?
This tool sorts the data and interpolates linearly between order statistics — the inclusive method (Excel's QUARTILE.INC / the R-7 rule). Q1 is the 25th percentile, Q2 the median, Q3 the 75th; the IQR is Q3 − Q1. Other methods exist and can differ slightly on small samples.
What is the difference between mean, median and mode?
The mean is the arithmetic average; the median is the middle value when sorted (robust to outliers); the mode is the most frequent value. When data is skewed, the median often describes the "typical" value better than the mean.
Can a data set have more than one mode?
Yes — if several values tie for the highest frequency the data is multi-modal, and this tool lists them all. If every value appears once there is no mode, shown as "none".