Descriptive Statistics Calculator

Descriptive statistics are numerical measures that summarize and describe the key features of a data set. They include measures of central tendency (mean, median, mode), measures of spread (standard deviation, variance, range), and measures of shape (skewness, kurtosis). Unlike inferential statistics, they describe only the data at hand rather than making predictions about a larger population.

When calculating for a population, you divide by n (the total count) to get variance and standard deviation. For a sample, you divide by n−1 (Bessel's correction) to produce an unbiased estimate of the population parameter. Use 'Sample' if your data is a subset drawn from a larger group, and 'Population' only if your data contains every member of the group.

You can type or paste numbers separated by commas, spaces, or line breaks. The calculator accepts integers and decimals. You can paste directly from a spreadsheet column — just copy the cells and paste them into the data entry box.

Standard deviation measures how spread out the values in a data set are around the mean. A low standard deviation means values are clustered close to the mean; a high standard deviation means they are spread over a wider range. It is expressed in the same units as the original data.

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). It represents the middle 50% of the data and is a robust measure of spread that is not affected by extreme values or outliers. Values more than 1.5 × IQR below Q1 or above Q3 are typically considered outliers.

Skewness measures the asymmetry of a distribution. A positive skew means the tail is longer on the right; a negative skew means it extends more to the left. Kurtosis (excess) measures the 'tailedness' relative to a normal distribution — positive values indicate heavier tails (leptokurtic), while negative values indicate lighter tails (platykurtic).

The coefficient of variation (CV) expresses standard deviation as a percentage of the mean. It allows you to compare the relative variability of data sets that have different units or very different means. A lower CV indicates more consistency, while a higher CV indicates more variability relative to the average.

The geometric mean is used when comparing values that are multiplicative or exponential in nature, such as growth rates, investment returns, or ratios. It is calculated as the nth root of the product of all n values and is always less than or equal to the arithmetic mean. It requires all values to be positive.