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How to Make Box and Whisker Plot for High-Impact Biomedical Data Analysis

CLYTE research team
4 days ago
5 min read

The Box and Whisker Plot (also known as a Box Plot) is a foundational visualization tool that unlocks profound insights into the distribution, spread, and skewness of quantitative data. In the demanding field of biomedical data analysis, where clear, transparent communication of clinical trial results, gene expression levels, or patient outcomes is critical, the box plot offers a streamlined, non-parametric alternative to histograms. By summarizing a dataset using just five key values, it allows researchers to instantly compare data distributions across multiple experimental or patient groups, facilitating robust statistical conclusions.

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The Essential Foundation: The Five-Number Summary

To construct a box plot, you must first calculate the Five-Number Summary. This set of values divides the entire dataset into four equal sections, with each section representing 25% of the data points.

Minimum Value: The smallest number in the dataset.
First Quartile (Q1): Also known as the lower quartile or the 25th percentile. This is the median of the lower half of the data, marking the point below which the lowest 25% of values fall.
Median (Q2): The middle value of the entire dataset, or the 50th percentile. If the dataset has an even number of values, the median is the average of the two middle numbers. This line inside the box shows the central tendency.
Third Quartile (Q3): Also known as the upper quartile or the 75th percentile. This is the median of the upper half of the data, marking the point below which 75% of values fall.
Maximum Value: The largest number in the dataset.

Step-by-Step Guide to Plot Construction

Creating the plot, whether manually or using statistical software (like Excel, R, or MedCalc, as seen in the references), follows a universal process based on these five numbers.

Step 1: Order and Calculate

The absolute first step for any box plot creation is to order your data from least to greatest. This sorting is essential for accurately identifying the Minimum, Maximum, and especially the Median and Quartiles. Once sorted, calculate the five-number summary as described above.

Step 2: Define the Interquartile Range (IQR)

The Interquartile Range (IQR) is the distance between the first and third quartiles (IQR = Q3 - Q1). The IQR defines the length of the box and contains the central 50% of your data. For researchers, this metric is often more robust than the total range, as it is less affected by extreme values.

Step 3: Identify and Plot Outliers (The Tukey Rule)

A critical feature, particularly in clinical data where aberrant patient responses or measurement errors may occur, is the ability to easily flag outliers.

The most common method uses the IQR rule:

A data point is considered an outlier if it is below Q1 - (1.5 * IQR) .
A data point is considered an outlier if it is above Q3 + (1.5 * IQR).

Outliers are typically marked as individual points (e.g., circles or asterisks) beyond the whiskers.

Step 4: Draw the Number Line, Box, and Whiskers

Create a Scale: Draw a number line that spans the entire range of your data, from a point below the Minimum to a point above the Maximum.
Draw the Box: Draw a rectangle from the location of Q1 to the location of Q3. This box represents the IQR.
Mark the Median: Draw a vertical line inside the box at the location of the Median (Q2).
Add the Whiskers: Draw a line segment (the "whisker") extending from the center of the box (Q1) to the Minimum value. Draw a second whisker from the box (Q3) to the Maximum value (or to the last non-outlier value).

Critical Applications in Biomedical Research

The box plot is indispensable for analyzing and presenting biomedical and clinical data because of its efficiency in comparing distributions.

Clinical Trials: When comparing the effectiveness of Drug A versus a placebo, side-by-side box plots can immediately reveal differences in central tendency (Median), variance (IQR box length), and the presence of extreme responders (Outliers).
Gene Expression: Researchers use box plots to compare the expression level of a specific gene across different tissue types (e.g., healthy vs. cancerous). The plot quickly illustrates which tissue exhibits a higher median expression and greater variability.
Statistical Clarity: By visually representing the five-number summary and potential outliers, the box plot helps satisfy the requirement for transparent reporting, moving beyond simple mean and standard deviation figures that can be easily skewed by non-normal distributions.

Frequently Asked Questions (FAQ) About Box Plot

How do you make a box and whisker plot step by step?

Creating a box and whisker plot, or box plot, involves seven core steps:

Order the Data: Arrange all numbers in your dataset from least to greatest.
Find the Minimum and Maximum: Identify the smallest and largest values in the ordered set.
Find the Median (Q2): Locate the exact middle value of the entire dataset.
Find the Quartiles (Q1 and Q3): Find the median of the lower half of the data (Q1) and the median of the upper half of the data (Q3).
Calculate the IQR: Determine the Interquartile Range (IQR = Q3 - Q1).
Identify Outliers (Optional but Recommended): Use the 1.5 * IQR rule to find any points outside the whiskers.
Draw the Plot: Create a number line, then draw the box from Q1 to Q3, a line for the median, and whiskers extending to the minimum and maximum (or to the last non-outlier value).

How to find Q1 and Q3 in a box plot?

Q1 (the First Quartile) and Q3 (the Third Quartile) are found by identifying the median of the two halves of your ordered dataset, as divided by the overall median (Q2):

Q1 (Lower Quartile): It is the median of the data points that fall below the overall median (Q2). It marks the beginning of the box.
Q3 (Upper Quartile): It is the median of the data points that fall above the overall median (Q2). It marks the end of the box.

Can Excel create a box and whisker plot?

Yes, Microsoft Excel has a built-in chart type for box and whisker plots.

In modern versions of Excel (2016 and later), you can select your raw data, go to the "Insert" tab, and find the "Box and Whisker" option under the Statistical Charts category.
Excel automatically calculates the median, quartiles, and outliers based on the data provided.

How to manually create a boxplot?

To create a boxplot manually:

Calculate the Five-Number Summary: Determine the Minimum, Q1, Median, Q3, and Maximum from your ordered dataset.
Draw a Number Line: Create a horizontal or vertical scale that covers the range from your Minimum to Maximum.
Mark the Five Numbers: Place a small vertical line or dot on your number line at the exact positions of Q1, the Median, and Q3.
Draw the Box: Connect the Q1 and Q3 marks with horizontal lines to form the rectangle (the box).
Draw the Whiskers: Draw a line segment (the whisker) from the Q1 line to the Minimum value, and another from the Q3 line to the Maximum value. (Adjust the whiskers to the last non-outlier data points if outliers are being plotted separately.)