Descriptive Statistics Calculator

What Is Descriptive Statistics?

Descriptive statistics summarize a dataset with measures of central tendency, dispersion, and shape. They help you understand how values cluster, spread, and skew without making inferences about a larger population. Use this calculator alongside the Five Number Summary Calculator and Standard Deviation Calculator for deeper analysis.

Measures Included

This tool reports the five-number summary (min, Q1, median, Q3, max), mean, mode, midrange, variance, standard deviation, standard error, range, IQR, outlier fences, skewness, and excess kurtosis. Choose sample or population mode to match your data context.

Skewness and Kurtosis

Skewness measures asymmetry: positive skew means a longer right tail, negative skew means a longer left tail. Excess kurtosis compares tail heaviness to a normal distribution. Values near zero indicate roughly symmetric, normal-like shape.

Example

For ten ages $30, 34, 30, 26, 38, 41, 30, 61, 38, 55$, the mean is $38.3$, the median is $36$, and the value $61$ may appear as an outlier above the upper fence.

Frequently Asked Questions

How many values do I need?

At least two numbers. Skewness needs three or more values; kurtosis needs four or more.

What is the difference between sample and population?

Sample mode divides variance by $n-1$ for unbiased estimation. Population mode divides by $n$ when your data represents the entire group.

How are outliers detected?

Values below $Q_1 - 1.5 \times \text{IQR}$ or above $Q_3 + 1.5 \times \text{IQR}$ are flagged as outliers using the standard Tukey fence rule.

What does excess kurtosis mean?

Excess kurtosis is kurtosis minus 3. Zero means normal-like tails; positive means heavier tails; negative means lighter tails.

Can a dataset have multiple modes?

Yes. When two or more values tie for highest frequency, all are listed as modes.

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