Statistics Calculator

Enter a list of numbers to calculate mean, median, mode, range, variance, standard deviation, quartiles, and more. Separate values with commas, spaces, or new lines.

How to Calculate Mean, Median, and Mode

Mean (average): add all values and divide by the count. For 2, 4, 6, 8: mean = (2+4+6+8)/4 = 5. Median (middle value): sort the data and find the middle value. For odd count, it is the exact middle. For even count, it is the average of the two middle values. For 1, 3, 7, 9: median = (3+7)/2 = 5. Mode: the value(s) that appear most often. A data set can have one mode, multiple modes, or no mode if all values appear equally.

Standard Deviation and Variance

Variance measures how far each data point is from the mean on average (squared). Standard deviation is the square root of variance — it is in the same units as the original data. This calculator shows both population standard deviation (σ, divides by n) and sample standard deviation (s, divides by n-1). Use population std dev when you have the entire population; use sample std dev when working with a sample.

Quartiles and Interquartile Range (IQR)

Quartiles divide sorted data into four equal parts. Q1 (first quartile) is the median of the lower half. Q2 is the overall median. Q3 (third quartile) is the median of the upper half. IQR = Q3 - Q1. The IQR measures the spread of the middle 50% of data and is used to identify outliers (values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR).

Mean is the arithmetic average (sum ÷ count). Median is the middle value when sorted. For skewed data (like income), median is more representative. For symmetrical data, they are similar.
Standard deviation measures how spread out numbers are from the mean. A low std dev means values are clustered around the mean. A high std dev means they are widely spread.
Interquartile Range (Q3-Q1) measures the middle 50% of data spread. It is used to detect outliers: values more than 1.5×IQR below Q1 or above Q3 are considered outliers.