Box and Whiskers Plot: Definition, Uses, How to Draw a Box and Whiskers Plot?

The box and whisker plot is referred to as the procedure to abstract a collection of data that is calculated using an interval scale. It is also known as a box plan. These are mostly used to interpret data. It is a form of graphical approach that shows how the data in a dataset changes over time. The data can alternatively be shown using a histogram. The histogram, on the other hand, is an adequate presentation. A box and whisker plot is favored over a histogram because it allows many sets of data to be presented in the same graph, providing more information this takes up less space, which is beneficial for comparing distributions across many groups or datasets. Here, we will be learning more about box and whiskers plots in detail and discussing some important questions related to them.

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Key Takeaways: Box and Whisker Plot, boxplot, statistics, histogram, elements of box-whisker-plot, uses of box and whisker plot.

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What is the Purpose of Using a Box and Whisker Plot? 

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Since they can consolidate data from various sources and present the conclusions in a single graph, box and whisker plots are particularly effective and easy to understand. Data from multiple categories may be compared using box and whisker plots, making decision-making easier and more effective.

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When do We Use a Box and Whisker Plot?

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When you have many data sets from different sources that are connected in any manner then we use box and whisker graphs. They are designed to show greater information at a glance, such as symmetry, skew, variance, and outliers for a set of data. It is simple to determine where the majority of the data is located and compare various categories. Various examples include

• Before and after data from a process modification 
• Camshaft lobes, for example, have similar characteristics on one portion. 
• The results from A test from people of the different classes but same course. 
• The data is collected from two alike devices or machines that produce the same kind of goods.

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Elements of a Box and Whisker Plot 

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• The Minimum Score: The lowest value after deleting outliers is the minimum score. 
• The Maximum Score: The greatest score after deleting outliers is the maximum score. 
• The median is the middle of a set of data that may be represented by a line that splits the box into two halves (it is at times also known as the second quartile). The majority of the scores are substantially higher or equal to the value, while half are lower. 
• The Lower Quartile: The lower quartile is also known as the first quartile, as it contains less than 25% of the total scores. 
• The Upper Quartile: The upper quartile, also known as the third quartile, is comprised of scores that are less than 75 percent of the total. 
• The Interquartile Range (sometimes known as the IQR (interquartile range)): The interquartile range is the center box plot that represents the scores ranging from 25% to 75%, or 50 current scores. 

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How to Draw a Box and Whisker Plot?

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To draw the box and whisker plot we use the elements of the box plots such as the minimum value, maximum value, median lower quartile, and upper quartile. We shall now explain this using an example.

Box and Whisker Plot

Given here is a sample of the weight of 9 boxes of almonds in grams: 

29, 30, 32, 35, 37, 39, 40, 42, 45. 

Solution

STEP 1: Make a box plot of the data, starting with the smallest and working your way up. However, the data, in this case, is already in ascending order. Through this, we get the minimum value which in this case is 29 and the maximum value which is 45. So let us go to the next phase. 

STEP 2: In this stage, find the median, Here the median for the given data is the number in the middle which is 37. 

STEP 3: We'll go on to the following phase, which is to determine the quartile. The first quartile (Q₁) is the median of all the elements or data points to the left of the median that is the median of {29,30,32,35}, which is 30+32/2 = 31. The third quartile (Q₃) is the median of the elements to the right of the median that is {39,40,42,45} which is 40+42/2 = 41. 

STEP 4: Now we find out the interquartile range which is the center box plot that represents the scores ranging from 25% to 75%, or 50 current scores.

Thus, the interquartile range is Q₃ – Q₁ = 41 – 31 = 10. 

The following is a five-number summary which is given by:

Minimum, Q₁, Median, Q₃, Maximum. 

As a result, the five-number summary for the provided data is

29, 31,37,41,45. 

Based on the five-number summary, we can now build the box and whisker plot. 

Box and Whisker Plot

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Things to Remember

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• A quartile is a statistical phrase for dividing observations into four predetermined ranges based on data values and how they relate to the total set of observations. 
• The procedure to abstract a collection of data that is calculated using an interval scale is termed a box and whisker plot. 
• Box and whisker plots are particularly effective and easy to understand. 
• Remember to learn the examples of the kinds of data on which we can implement box plots. 
• Elements of the box plot take the most priority. 

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