What is the five-number summary?

Minimum, Q1 (25th percentile), median (50th), Q3 (75th), and maximum. These five values describe the spread and centre of any dataset.

The Interquartile Range = Q3 − Q1. It captures the spread of the middle 50% of data and is resistant to outliers.

What does skewness tell me?

Skewness measures the asymmetry of the distribution. Positive = right tail longer (outliers high). Negative = left tail longer (outliers low). Near 0 = roughly symmetric.

Statistics Calculator

Enter a dataset to get a complete descriptive statistics report: five-number summary (min, Q1, median, Q3, max), IQR, mean, variance, standard deviation, and skewness coefficient.

How to use this calculator

Enter your data values separated by commas or spaces.
Read the five-number summary (boxplot inputs), IQR, mean, SD, and skewness all at once.
For focused mean/median/mode outputs, use the Mean, Median, Mode Calculator.
For standard deviation only, use the Standard Deviation Calculator.

Formula & method

Five-number summary, IQR and skewness

Q1 = 25th percentile · Q3 = 75th percentile · IQR = Q3 − Q1 · Skewness = [N/((N−1)(N−2))] Σ((xᵢ−x̄)/s)³

Percentiles use linear interpolation. Skewness uses the Fisher-Pearson coefficient.

Example

[4,8,15,16,23,42,50,60,75]: Q1=11.5, Median=23, Q3=55, IQR=43.5, Mean=32.56, SD=25.1.

Key insights

The five-number summary (min, Q1, median, Q3, max) is the basis of a boxplot.
IQR = Q3 − Q1 identifies the middle 50% of data — robust to outliers.
Outliers can be defined as values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR (Tukey fences).
Skewness = 0 indicates a symmetric distribution; positive skew means right-heavy; negative means left-heavy.

How to interpret your result

IQR and outlier detection

Values outside 1.5 × IQR from the quartiles are potential outliers. The IQR is more robust than range for datasets with extreme values.

Skewness

Fisher-Pearson skewness: |skewness| < 0.5 ≈ symmetric, 0.5–1 ≈ moderate skew, > 1 = high skew.

Scope of this calculator

This tool provides a comprehensive summary across all descriptive measures. For a focused analysis of central tendency, use Mean, Median, Mode; for dispersion focus, use Standard Deviation Calculator.

Frequently asked questions

What is the five-number summary?: Minimum, Q1 (25th percentile), median (50th), Q3 (75th), and maximum. These five values describe the spread and centre of any dataset.
What is IQR?: The Interquartile Range = Q3 − Q1. It captures the spread of the middle 50% of data and is resistant to outliers.
What does skewness tell me?: Skewness measures the asymmetry of the distribution. Positive = right tail longer (outliers high). Negative = left tail longer (outliers low). Near 0 = roughly symmetric.

Related calculators

Mean, Median, Mode, Range Calculator — Calculate mean (average), median, mode, and range for any dataset — the four pillars of descriptive statistics.
Standard Deviation Calculator — Calculate sample and population standard deviation, variance, standard error, and coefficient of variation for any dataset.
Z-score Calculator — Convert a raw score to a Z-score (standard score), find its percentile, and compute cumulative probability under the normal distribution.

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