Summary Statistics Calculator

Descriptive statistics are numeric summaries that 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 positional measures (quartiles, min, max). They help you quickly understand the shape and distribution of your data without drawing broader conclusions about a population.

Population standard deviation divides the sum of squared deviations by N (the total count), while sample standard deviation divides by N−1 (known as Bessel's correction). Use population when your data represents the entire group you're studying. Use sample when your data is a subset and you're estimating the true population variability — this correction reduces bias in the estimate.

Type or paste numbers separated by commas, spaces, or new lines. For example: '4, 7, 13, 2, 1' or '4 7 13 2 1'. You can copy a column directly from a spreadsheet application like Excel or Google Sheets and paste it into the data field — the calculator will parse it automatically.

The IQR is the difference between the third quartile (Q3, 75th percentile) and the first quartile (Q1, 25th percentile). It measures the spread of the middle 50% of your data and is resistant to outliers. A larger IQR indicates greater variability in the central portion of the data set.

The median is the middle value of a sorted data set, while the mean is the arithmetic average. The median is not affected by extreme outliers or skewed data, making it a better measure of central tendency when your data has large outliers. If the mean and median differ significantly, your data is likely skewed.

The midrange is the average of the minimum and maximum values in a data set — calculated as (Min + Max) / 2. It gives a quick sense of the center of the data's full extent, but it is highly sensitive to outliers since it relies entirely on the two most extreme values.

Yes. You can paste data sets with hundreds or thousands of values directly from a spreadsheet. The calculator processes all values and generates the full set of summary statistics. For very large data sets, pasting from a spreadsheet column (one value per line) is the easiest input method.

When a data set has multiple values that appear with equal highest frequency, it is called multimodal. This calculator reports the smallest modal value in the Mode field. If all values appear exactly once (no repeats), there is no mode — the calculator will display 'N/A' in that case.