Statistics Calculator

Understanding Descriptive Statistics

Descriptive statistics summarize and describe the main features of a dataset. Rather than analyzing every individual data point, descriptive statistics condense the information into a few key numbers that tell you what is typical, how spread out the data is, and what the shape of the distribution looks like. This calculator computes all the essential measures instantly as you type or paste your data.

Measures of Central Tendency

Central tendency tells you where the "center" of your data lies. The three main measures are the mean, median, and mode. The mean (arithmetic average) is calculated by summing all values and dividing by the count. It uses every data point, which makes it comprehensive but also sensitive to extreme values (outliers). The median is the middle value when data is sorted. For an even number of values, it is the average of the two middle values. The median is resistant to outliers, making it preferable for skewed distributions like income data or house prices. The mode is the most frequently occurring value. Unlike mean and median, the mode can be used with categorical data and a dataset can have multiple modes or no mode at all.

Measures of Spread

Spread (or dispersion) tells you how much values differ from the center. The range is the simplest measure: maximum minus minimum. It is easy to understand but sensitive to outliers. Standard deviation measures the average distance of each data point from the mean. A small standard deviation means values cluster tightly around the mean; a large one means they are spread out. In a normal distribution, roughly 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three (the 68-95-99.7 rule). Variance is the square of the standard deviation. The interquartile range (IQR) is Q3 minus Q1, representing the range of the middle 50% of the data. The IQR is robust to outliers and is used to construct box plots and identify outliers (values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR).

Sample vs. Population Standard Deviation

This calculator reports both sample and population standard deviation. Use the population standard deviation (divides by N) when your data includes the entire group you are studying. Use the sample standard deviation (divides by N-1, known as Bessel's correction) when your data is a subset of a larger population, which is the more common case in practice. The sample version is slightly larger because it accounts for the uncertainty of estimating from incomplete data.