Math

Statistics Calculator

Enter a set of numbers to calculate count, sum, mean, median, mode, range, quartiles, IQR, standard deviation, and percentiles.

Quick Answer

Enter comma-separated numbers to get a full descriptive statistics summary including measures of central tendency (mean, median, mode), spread (range, IQR, standard deviation), and position (quartiles, percentiles).

Enter Your Data

Separate numbers with commas, spaces, or new lines.

About This Tool

The Statistics Calculator provides a comprehensive descriptive statistics summary for any dataset. Enter numbers separated by commas and instantly see measures of central tendency, dispersion, and position. This tool is ideal for students, researchers, and data analysts who need quick statistical analysis without spreadsheet software.

Measures of Central Tendency

Mean, median, and mode each describe the center of your data differently. The mean is sensitive to extreme values, making the median more robust for skewed distributions. Mode identifies the most common value and is the only measure that works for categorical data. For normally distributed data, all three converge to the same value.

Measures of Spread

Range gives the simplest measure of spread but is heavily influenced by outliers. IQR (interquartile range) is more robust, capturing the middle 50% of data. Standard deviation quantifies the average distance from the mean, making it the most commonly used measure of variability in statistical analysis.

Frequently Asked Questions

What is the difference between mean, median, and mode?
Mean is the average (sum / count). Median is the middle value when data is sorted. Mode is the most frequently occurring value. For symmetric distributions all three are similar. For skewed data, the median is a better measure of center than the mean because it is not affected by extreme values (outliers).
What are quartiles and IQR?
Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 is the median (50th percentile), and Q3 (75th percentile) is the median of the upper half. The Interquartile Range (IQR) = Q3 - Q1, representing the middle 50% of data. IQR is used to identify outliers: values below Q1-1.5*IQR or above Q3+1.5*IQR are considered outliers.
What is standard deviation?
Standard deviation measures how spread out values are from the mean. A small standard deviation means data points cluster near the mean. A large standard deviation means data is spread over a wider range. In a normal distribution, about 68% of data falls within 1 standard deviation of the mean, and 95% within 2 standard deviations.
When should I use population vs sample statistics?
Use population statistics (divide by N) when you have data for the entire group. Use sample statistics (divide by N-1) when your data is a sample from a larger population. This calculator uses population variance and standard deviation. For sample standard deviation, multiply by sqrt(N/(N-1)).
What is a percentile?
A percentile indicates the value below which a given percentage of observations fall. The 90th percentile means 90% of values are at or below that number. Percentiles are commonly used in standardized testing (SAT scores), growth charts (baby weight/height), and performance benchmarks.

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