Box Plot Calculator

Understanding Box and Whisker Plots

A box plot (or box-and-whisker diagram) provides a standardized graphical representation of dataset distribution based on a five-number summary: minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum.

Five-Number Summary and Formulas

Key statistics used to construct a box plot include:

• Minimum ($Min$): The lowest value excluding statistical outliers.
• First Quartile ($Q_1$): The $25^{\text{th}}$ percentile mark dividing lower $25\%$ of data.
• Median ($Q_2$): The $50^{\text{th}}$ percentile mark representing the middle value.
• Third Quartile ($Q_3$): The $75^{\text{th}}$ percentile mark dividing upper $25\%$ of data.
• Interquartile Range ($IQR$): The distance between $Q_3$ and $Q_1$, calculated as $IQR = Q_3 - Q_1$.
• Outlier Fences: Values below $Q_1 - 1.5 \times IQR$ or above $Q_3 + 1.5 \times IQR$ are flagged as outliers.

Interpreting Box Plots

The central rectangle spans from $Q_1$ to $Q_3$, containing the middle $50\%$ of your data. The line inside the box marks the median. Whiskers extend outward to show variability outside the upper and lower quartiles, while individual points beyond whiskers represent potential outliers.

Related Tools

Explore related tools to assist with your calculations:

• Scatter Plot Maker
• Stem and Leaf Plot Generator