Box &amp; Whisker plot is an easy-to-use representative tool that can be used for the description of data in numeric form. It includes minimum, first quartile, median, third quartile, and maximum for providing the five number summary of the dataset.&nbsp;The chart will help show variation, comparison of groups, and even identify possible outliers in one glance. Box and whisker plots have broad applications in statistics, quality improvement, manufacturing, research, education, and business analysis with the comparison of data distributions.<h2 id="d666374d-06e0-44a2-8b60-da23616a19e2" data-toc-id="d666374d-06e0-44a2-8b60-da23616a19e2" style="margin-top: 18pt; margin-bottom: 4pt; text-align: left; font-size: 24px; line-height: 1.2;">What Is a Box and Whisker Plot?</h2>A box and whisker plot is often called a box plot. It summarizes a dataset using five key values: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. These values collectively are known as the five-number summary. The box moves&nbsp; from Q1 to Q3, while a line inside the box marks the median. Whiskers headed toward the lower and upper ends of the distribution.This plot shows where observation concentrated at one spot and how the variation takes place. Several box plots can share one scale That makes group differences easier to spot than in a table.<h2 id="ab6bfb74-4f24-4ab3-9a2f-02f4672bf099" data-toc-id="ab6bfb74-4f24-4ab3-9a2f-02f4672bf099" style="margin-top: 18pt; margin-bottom: 4pt; text-align: left; font-size: 24px; line-height: 1.2;">Five-Number Summary Explained</h2><div style="display: flex;"><img src="https://ezycourse.b-cdn.net/3211/cmv06rvxobgdh01xx16yf4wbq.png" alt="image" style="position: relative; width: 389px; height: auto; cursor: pointer; margin: 0px auto;"></div>This can be explained by the following description for the five-number summary:<ul style="margin-top: 0px; margin-bottom: 0px; padding-inline-start: 48px;"><li aria-level="1" style="color: rgb(0, 0, 0); list-style-type: disc; font-size: 11pt; font-family: Arial, sans-serif; background-color: transparent; font-variant: normal; vertical-align: baseline; white-space: pre;">Minimum: The smallest value observed in the data set.</li><li aria-level="1" style="color: rgb(0, 0, 0); list-style-type: disc; font-size: 11pt; font-family: Arial, sans-serif; background-color: transparent; font-variant: normal; vertical-align: baseline; white-space: pre;">Q1: The point beyond which the first quarter of the sorted data lies.</li><li aria-level="1" style="color: rgb(0, 0, 0); list-style-type: disc; font-size: 11pt; font-family: Arial, sans-serif; background-color: transparent; font-variant: normal; vertical-align: baseline; white-space: pre;">Median: The midpoint of the sorted data set, dividing it into two halves of equal number.</li><li aria-level="1" style="color: rgb(0, 0, 0); list-style-type: disc; font-size: 11pt; font-family: Arial, sans-serif; background-color: transparent; font-variant: normal; vertical-align: baseline; white-space: pre;">Q3: The point beyond which the last quarter of the sorted data lies.</li><li aria-level="1" style="color: rgb(0, 0, 0); list-style-type: disc; font-size: 11pt; font-family: Arial, sans-serif; background-color: transparent; font-variant: normal; vertical-align: baseline; white-space: pre;">Maximum: The largest value observed in the data set.</li><li aria-level="1" style="color: rgb(0, 0, 0); list-style-type: disc; font-size: 11pt; font-family: Arial, sans-serif; background-color: transparent; font-variant: normal; vertical-align: baseline; white-space: pre;">The difference between Q1 and Q3 is known as the Inter-Quartile Range (IQR) and is obtained from:</li></ul>IQR = Q3 − Q1This represents the middle 50% of the data points.<h2 id="555eccd4-a078-4cf9-a452-34f28b9f8971" data-toc-id="555eccd4-a078-4cf9-a452-34f28b9f8971" style="margin-top: 18pt; margin-bottom: 4pt; text-align: left; font-size: 24px; line-height: 1.2;">How to Make a Box and Whisker Plot?</h2><div style="display: flex;"><img src="https://ezycourse.b-cdn.net/3211/cmv06tk3cbjo001y16iuy5c91.png" alt="image" style="position: relative; width: 397px; height: auto; cursor: pointer; margin: 0px auto;"></div>The process of making a box plot involves ordering the observations from lowest to highest. Median is found, and Q1 and Q3 are calculated based on the selected quartile definition. The minimum and maximum are found and the five numbers are placed on a number line.A box is drawn from Q1 to Q3, with a line for the median. For a standard box plot, the whiskers go to the minimum and maximum. In a modified box plot, the whiskers typically go to the farthest observations that are within 1.5 × IQR of the quartiles. Any other values are shown separately as outliers.Quartile definitions vary among software programs, so it is important to use one consistently.How to Read a Box and Whisker PlotLook at the median first to see how centrally located it is. Next look at the box. A small box means that the middle 50% of the observations are closely clustered, whereas a larger box means more dispersion.The placement of the median within the box can give some hints on the shape of the distribution. For instance, if the median is closer to one quartile, this could mean that the distribution is not symmetric.Lastly, outliers should receive individual attention. Any observation outside the whisker range could mean either an anomaly, measurement error, unique operating conditions, or just natural process dispersion. Thus, any outlier needs to be investigated.<h2 id="b89c4f52-a839-4770-9e29-6f72c35fc73b" data-toc-id="b89c4f52-a839-4770-9e29-6f72c35fc73b" style="margin-top: 18pt; margin-bottom: 4pt; text-align: left; font-size: 24px; line-height: 1.2;">Why Use Box and Whisker Plots?</h2>Box and Whisker plots can be used to compare distributions between different groups. For example, in quality improvement, one might use box plots to compare shaft diameters for three machines. One machine could have a higher median, another could have a larger IQR, and a third could have outliers at both extremes.Box plots are useful in manufacturing, quality control, process improvement, education, research, and business analytics.<h2 id="ce926186-f785-4cc6-946d-e0543b68d6e4" data-toc-id="ce926186-f785-4cc6-946d-e0543b68d6e4" style="margin-top: 18pt; margin-bottom: 4pt; text-align: left; font-size: 24px; line-height: 1.2;">Uses of Box and Whisker Plot in Business and Manufacturing</h2>In business, box and whisker plots allow for comparisons among sales, delivery time, response time of customers, or employees' performance. For instance, one could compare delivery times between different branches and be able to determine any variations or delays.In manufacturing, box plots can be used to compare various measures such as dimensions of products, cycle times, defect rate, and production volumes. For instance, a quality engineer could compare the diameters of shafts produced by different machines. A wide box suggests more variation while an outlier suggests some special circumstances in production or measuring. Box Plot vs Histogram<div style="display: flex;"><img src="https://ezycourse.b-cdn.net/3211/cmv06wjocbl3r01y1cw427ngo.png" alt="image" style="position: relative; width: 391px; height: auto; cursor: pointer; margin: 0px auto;"></div>A histogram represents the frequency of observations in numerical ranges and thus helps in studying the general shape of the distribution. A box plot represents the distribution in a more compact way. Therefore it is more convenient to use when comparing multiple groups.A histogram can help identify clusters and gaps, while a box plot makes it easy to compare the median, quartiles, range, and outliers.<h2 id="abab1f17-695a-4f10-92b1-6e6667a332f5" data-toc-id="abab1f17-695a-4f10-92b1-6e6667a332f5" style="margin-top: 18pt; margin-bottom: 4pt; text-align: left; font-size: 24px; line-height: 1.2;">Final Takeaway</h2>The Box and Whisker plot summarizes the data graphically in terms of center, spread, and extremes. Through the graphical display of the median, interquartile range, whiskers, and outliers, one is able to compare the groups in a manner that would not be possible from looking at the data. This is a useful quality tool.

Learn what a box and whisker plot is, explore examples and practical uses, and discover how to read quartiles, medians, variation, and outliers.

Box and Whisker Plot: Definition, Examples, Uses & How to Read One?

Uses of Box and Whisker Plot in Business and Manufacturing

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Box and Whisker Plot: Definition, Examples, Uses & How to Read One?

Box and Whisker Plot: Definition, Examples, Uses & How to Read One?

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