Data visualization is a crucial aspect of any data analysis or presentation. It allows us to quickly and easily understand patterns and trends in the data and make informed decisions based on this information. One helpful tool for visualizing data is the box and whisker plot, also known as a box plot. This type of plot displays data distribution in a compact and easy-to-interpret format, making it a valuable tool for data exploration and comparison. In this article, we will delve into the basics of box and whisker plots and how to interpret and use them to visualize your data effectively.

## Box and Whisker Plot

A box and whisker plot, also known as a box plot, is a graphical representation of the distribution of numerical data. It is a way of showing the distribution of data by displaying the minimum value, first quartile (Q1, or 25th percentile), median (Q2, or 50th percentile), third quartile (Q3, or 75th percentile), and maximum value of the data set. These values are plotted on a number line, with a box drawn around the first quartile, median, and third quartile, and whiskers extending from the box to the minimum and maximum values.

The box in a box and whisker plot represents the middle 50% of the data, with the median (Q2) dividing the box into two equal parts. The bottom of the box represents the first quartile (Q1), the value below which 25% of the data falls. The top of the box represents the third quartile (Q3), the value below which 75% of the data falls. The whiskers extend from the box to the minimum and maximum values of the data set.

Box and whisker plots help compare the distributions of multiple data sets and identify potential outliers in a data set. They are also helpful in showing data distribution's skewness (asymmetry).

## Outliers (1.5 IQR Limit)

An outlier in a box and whisker plot is a data point that falls outside the expected range of the data. In a box and whisker plot, outliers are typically represented by dots or small circles that are plotted outside the whiskers of the box plot. These points are considered significantly different from the rest of the data in the set and can indicate the presence of errors or unusual observations in the data.

It is important to note that outliers in a data set do not necessarily indicate a problem with the data. Outliers can occur naturally in data sets and may not necessarily be due to errors or unusual observations. However, it is often helpful to investigate outliers further to determine whether they are valid data points or whether they may indicate a problem with the data collection or analysis process.

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of a data set. Some software (e.g. Minitab) limits the length of the whiskers in a box and whisker plot to 1.5 times the data set's interquartile range (IQR). Any point outside that limit is considered an outlier.

For example, if the IQR of a data set is 10, the whiskers in the box plot would extend to 15 (1.5 times 10) above Q3 and 15 below Q1. Any data points that fall outside this range would be considered outliers and plotted as individual points or small circles outside the whiskers of the box plot.

## Draw a Box and Whisker Plot using Excel

The below snapshot provides various steps to draw a Box and Whisker Plot using Microsoft Excel.

## Conclusion

In conclusion, the box and whisker plot is a powerful tool for visualizing data and understanding its distribution. It provides a concise and easy-to-interpret representation of the data, allowing us to identify patterns quickly.