Drawing a Box-and-Whisker Plot In Exercises 1...

Question

Drawing a Box-and-Whisker Plot In Exercises 15–18,

(b) draw a box-and-whisker plot that represents the data set.

39 36 30 27 26 24 28 35 39 60 50 41 35 32 51

Accepted Answer

Hello. In this video, we are going to be using the following data to draw a box and whisker plot that represents the data set. Now, the first thing we want to do is you want to organize the data set from least to greatest. Now, the data set is given to us from least to greatest already, so there are a few things we need to identify for a box and whisker plot. The first thing we need to identify is our minimum value. The minimum is the smallest value in the data set, and that is going to be 22. Next, we need to identify our maximum value. Our maximum value is the largest value in the data set, and that is going to be 57. Next, we are going to identify our median of the data set, and that is going to be considered our second quartile for the for the box and whisker plots. Now, the median is the minimal value of the data set, and since we have a total data set of 15 values, the median is going to be the 8th value, and that is going to be 40. So, our second quartile for the box and whisker plot is 40. Next, we are going to identify our first quartile. Now, quartile 1 is going to be defined as the median of the first of the lower half of the data set. Now, the median of the lower half of the data set is going to be 30. So our first quartile is defined as 30. Next, we're going to identify our 3rd quartile. Now, the 3rd quartile is the median of the upper half of the data set. Now, that median is going to be 50, so we have a 3rd quartile of 50. Now that we have our quartiles, let's go ahead and define or identify the interquartile range. Now, the interquartile range is defined as quartile 3 minus quartile 1. That is going to be 50 minus 30, and that is going to give us an interquartile range of 20. Now that we have the interquartile range, we are going to identify the lower and upper bounds, starting with the lower bound. Now, the lower bound of our box and whisker plot is defined as quartile 1 minus 1.5 multiplied by our interquartile range. That is going to be 30 minus 1.5, multiplied by 20. And by simplifying, that is going to give us a lower bound of zero. Finally, we need to identify the upper bound for the box and whisker plot. The upper bound is defined as quartile 3 plus 1.5 multiplied by the interquartile range. That is going to be 50 plus 1.5, multiplied by 20, and that is going to simplify to give us an upper bound of 80. Now, we need to identify if the minimum and maximum values are going to be inside of the box and whisker plot, so that we can identify any outliers. Now, our minimum value is at 0. our lower bound is 0, and our upper bound of the box and whisker plot is 80. So, are both the minimum and maximum values between 0 and 80? Well, the answer to that is yes, and since our minimum and maximum values are within this range, that means that there are going to be no outliers to the box and whisker plot. Finally, we are going to plot all the information on the box and whisker plot, and that is going to give us the following graph. So this is going to be the box and whisker plot that plots all the information that we just solved for, and this is going to be the solution to the problem. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Drawing a Box-and-Whisker Plot In Exercises 15–18,
(b) draw a box-and-whisker plot that represents the data set.

39 36 30 27 26 24 28 35 39 60 50 41 35 32 51

Key Concepts

Box-and-Whisker Plot

Quartiles

Interquartile Range (IQR)

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