π Statistics Calculator
Enter a set of numbers to instantly calculate mean, median, mode, variance, standard deviation, quartiles, and more.
Data Set
Your Result
How the Statistics Calculator Works
This calculator computes common descriptive statistics for any data set, helping you understand its central tendency, spread, and distribution.
Formulas
Population Variance = Ξ£(x β mean)Β² / n
Population Standard Deviation = βvariance
Quartiles use linear interpolation: index = p Γ (n β 1)
IQR = Q3 β Q1
Worked Example
The calculator loads with the data set 4, 8, 15, 16, 23, 42, 8, 15 (8 values). The sum is 131, giving a mean of 131 Γ· 8 = 16.375. Sorted, the values are 4, 8, 8, 15, 15, 16, 23, 42, so the median (average of the two middle values) is (15 + 15) Γ· 2 = 15, and the mode is 8 and 15 (each appears twice). The population variance is 124.7344 and the population standard deviation is β124.7344 β 11.1685. The first quartile is 8, the third quartile is 17.75, giving an IQR of 9.75.
Frequently Asked Questions
What's the difference between population and sample standard deviation?
Population standard deviation divides by n (the total count), assuming your data is the entire population. Sample standard deviation divides by nβ1 to correct for bias when your data is only a sample. This calculator uses the population formula.
How is the interquartile range (IQR) useful?
IQR measures the spread of the middle 50% of your data and is useful for identifying outliers β values are often considered outliers if they fall more than 1.5ΓIQR below Q1 or above Q3.
What if my data has no mode?
If every value appears exactly once, there is no mode. If multiple values tie for the highest frequency, all of them are shown as modes.