Statistics Calculator (Descriptive)

Descriptive statistics are numerical summaries that describe the key characteristics of a dataset. They include measures of central tendency (mean, median, mode), measures of spread (standard deviation, variance, range, IQR), and measures of shape (skewness). Unlike inferential statistics, they describe only the data you have — not predictions or inferences about a broader population.

When your data represents a sample taken from a larger population, the standard deviation is calculated by dividing by (n−1) — known as Bessel's correction — to produce an unbiased estimate. When your data is the entire population, you divide by n. If you're unsure, 'Sample' is usually the safer choice for real-world datasets.

Type or paste your numbers into the data input box separated by commas, spaces, or new lines. The calculator automatically cleans the input and ignores any non-numeric characters. You can also paste data directly from a spreadsheet column and it will be parsed correctly.

The Interquartile Range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1). It represents the middle 50% of your data and is a robust measure of spread that is not affected by outliers. It is commonly used to detect outliers: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are considered potential outliers.

Whether to exclude outliers depends on context. If an outlier is due to a data entry error, it should be corrected or removed. If it's a legitimate extreme value, removing it can distort your analysis. Always investigate the cause of an outlier before deciding to exclude it. Using the median and IQR instead of the mean and standard deviation provides outlier-resistant summaries.

Skewness measures the asymmetry of your data's distribution. A skewness near 0 indicates a roughly symmetric distribution. Positive skewness means the tail is longer on the right (higher values), while negative skewness means the tail extends to the left (lower values). A skewness value between −0.5 and 0.5 is generally considered approximately symmetric.

The median is the middle value when data is sorted in ascending order. If there is an odd number of values, the median is the exact middle value. If there is an even number of values, the median is the average of the two middle values. Unlike the mean, the median is not affected by extreme values, making it a better measure of center for skewed distributions.

A dataset can have one mode (unimodal), two modes (bimodal), or multiple modes (multimodal). If every value appears the same number of times, the dataset has no mode. This calculator reports all modes found in the dataset. A multimodal distribution may indicate the presence of distinct subgroups within your data.