Descriptive Statistics Calculator — Mean, Median, Mode, IQR & More

The Formula

Descriptive statistics summarize a dataset using measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation, IQR). The mean is the arithmetic average, the median is the middle value when sorted, the mode is the most frequent value, the variance measures the average squared deviation from the mean, the standard deviation is its square root, and quartiles divide the sorted data into four equal parts.

Variable Definitions

How to Use This Calculator

1. 1

   Enter your dataset in the text area, separating numbers by commas, spaces, semicolons, or line breaks.

2. 2

   The calculator automatically computes all major descriptive statistics including mean, median, mode, range, variance, standard deviation, and quartiles.

3. 3

   Review the highlighted results (mean, median, and standard deviation) for a quick summary of central tendency and spread.

4. 4

   Use the quartile values (Q1, Q3, IQR) to understand the data distribution and identify potential outliers (values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR).

5. 5

   Compare the mean and median values — a large difference between them indicates a skewed distribution.

Quick Reference

Common Applications

• Summarizing test scores and student performance data in educational assessment
• Analyzing survey responses and customer satisfaction ratings in market research
• Monitoring process quality metrics and manufacturing tolerances in quality control
• Describing patient vital signs and lab results in clinical research and healthcare analytics
• Evaluating financial returns, portfolio risk, and economic indicators in finance and economics

Box plot visualization of the five-number summary with formulas for key descriptive statistics

Understanding the Concept

Descriptive statistics form the foundation of data analysis by providing concise summaries of large datasets. The mean (arithmetic average) is the most common measure of central tendency, but it is sensitive to outliers — a single extreme value can pull the mean significantly in one direction. The median provides a robust alternative that is unaffected by outliers, making it the preferred measure for skewed distributions such as income data or housing prices. The mode is useful for categorical and discrete data, identifying the most common value(s). For dispersion, the range (max − min) gives a quick but crude measure of spread, while the interquartile range (IQR = Q3 − Q1) describes the spread of the middle 50% of the data, making it resistant to outliers. VarianceThe average of squared differences from the mean. The square root of variance gives the standard deviation. and standard deviation quantify the average distance of data points from the mean: a small standard deviation means values cluster tightly around the mean, while a large one means they are spread out. In a normal distribution, approximately 68% of data falls within ±1 standard deviation, 95% within ±2, and 99.7% within ±3 (the empirical rule). Quartiles divide the sorted data into four equal parts: Q1 (25th percentile), Q2 / median (50th percentile), and Q3 (75th percentile). The IQR is the standard measure used in box plots and for outlier detection via the 1.5×IQR rule.

Frequently Asked Questions

Sources & References