# Box Plot Analysis Calculator

Free box plot calculator. Enter data to get the five-number summary, IQR, fences, and outlier detection for box-and-whisker plot construction.

## What this calculates

Enter up to 10 data values to calculate the complete five-number summary (min, Q1, median, Q3, max), interquartile range, fences, and detect outliers for box-and-whisker plot analysis.

## Inputs

- **Number of Values** — min 4, max 10 — How many values to analyze (4-10). Need at least 4 for quartiles.
- **Value 1** — Data point 1.
- **Value 2** — Data point 2.
- **Value 3** — Data point 3.
- **Value 4** — Data point 4.
- **Value 5** — Data point 5.
- **Value 6** — Data point 6.
- **Value 7** — Data point 7.
- **Value 8** — Data point 8.
- **Value 9** — Data point 9.
- **Value 10** — Data point 10.

## Outputs

- **Minimum** — Smallest value in the dataset.
- **Q1 (25th Percentile)** — First quartile - median of lower half.
- **Median (Q2)** — Middle value of the sorted dataset.
- **Q3 (75th Percentile)** — Third quartile - median of upper half.
- **Maximum** — Largest value in the dataset.
- **IQR** — Interquartile range (Q3 - Q1).
- **Lower Fence** — Q1 - 1.5 x IQR. Values below this are outliers.
- **Upper Fence** — Q3 + 1.5 x IQR. Values above this are outliers.
- **Outliers** — formatted as text — Values outside the fences.

## Details

A box plot (box-and-whisker plot) is a standardized way to display data distribution based on the five-number summary. The box spans from Q1 to Q3 (containing the middle 50% of data), with a line at the median. Whiskers extend to the smallest and largest values within the fences.

Quartile calculation: The data is sorted and split at the median. Q1 is the median of the lower half, Q3 is the median of the upper half. The IQR (Q3 - Q1) measures the spread of the middle 50%. This calculator uses the exclusive method (median excluded from halves for odd n), which is the most common textbook approach.

Outlier detection: Values below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR are flagged as outliers. The 1.5 multiplier is Tukey's standard; values beyond 3 x IQR are considered extreme outliers. Outliers are plotted as individual points beyond the whiskers.

## Frequently Asked Questions

**Q: Why use 1.5 x IQR for outlier fences?**

A: John Tukey chose 1.5 x IQR as a practical threshold that flags approximately 0.7% of data as outliers for normally distributed data (about 1 in 150 points). Values beyond 3 x IQR are 'extreme outliers' (about 1 in 425,000 for normal data). The choice of 1.5 balances sensitivity with specificity.

**Q: What is the difference between this and the Five-Number Summary calculator?**

A: This calculator works directly with your raw data values and computes quartiles from the actual data. The Five-Number Summary calculator estimates the five numbers from a normal distribution's mean and standard deviation. Use this calculator when you have actual data points.

**Q: How do I interpret a box plot?**

A: The box shows the middle 50% of data (IQR). A line inside marks the median. If the median is off-center, the data is skewed. Long whiskers indicate spread. Points beyond whiskers are outliers. Comparing box plots side-by-side reveals differences in center, spread, and symmetry between groups.

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Source: https://vastcalc.com/calculators/statistics/box-plot
Category: Statistics
Last updated: 2026-04-21