Descriptive Statistics Calculator

Frequently Asked Questions

What are descriptive statistics?

Numbers that summarize a dataset: measures of center (mean, median, mode), spread (range, variance, SD, IQR), and shape (skewness, kurtosis).

What are quartiles and the IQR?

Q1, Q2 (median), Q3 split sorted data into four equal groups. IQR = Q3 − Q1 covers the middle 50% and is robust to outliers.

How is an outlier typically defined?

A common rule: any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. Box plots use this to flag outliers visually.

Why report multiple statistics instead of just the mean?

A single number hides the distribution. Two datasets can share a mean but differ wildly in spread and shape - Anscombe's quartet is the classic example.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

Enter a list of numbers separated by commas or spaces and this calculator computes a full suite of descriptive statistics in one click: central tendency (mean, median, mode), spread (standard deviation, variance, range, IQR), distribution shape (skewness), and the five-number summary used in box plots.

Key Statistical Measures

Mean: Arithmetic average. Sum divided by count. Sensitive to outliers.

Median: Middle value when sorted. Robust to outliers - preferred for skewed data.

Mode: Most frequent value(s). Useful for categorical and discrete data.

Standard deviation (s): Average distance of each value from the mean. This calculator uses the sample formula dividing by n−1 (Bessel's correction) for unbiased estimation.

Variance (s²): The square of the standard deviation. Used in many statistical tests but in squared units, so standard deviation is more interpretable.

IQR (Interquartile Range): Q3 − Q1. The spread of the middle 50% of data. Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are potential outliers by Tukey's rule.

CV (Coefficient of Variation): Standard deviation divided by mean, expressed as a percentage. Allows comparing variability across datasets with different units or scales.

Skewness: Measures asymmetry. Positive skew means a long right tail (most values are low but a few are very high). Negative skew means a long left tail.

Population vs. Sample Statistics

Population statistics (σ, μ) describe an entire group and divide variance by n. Sample statistics (s, x̄) describe a subset used to estimate the population and divide variance by n−1. This calculator computes sample statistics, which is the correct choice when your data is a sample drawn from a larger population.

Descriptive Statistics Calculator

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