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.

2 7 1 3 1 2 8 9 9 2 5 4 7 3 7 5 4

2 3 5 9 5 6 3 9 3 4 9 8 8 2 3 9 5

Accepted Answer

Hello. In this video, we are going to be drawing a box and whisker plot for the given data set. Now, before we draw our box of whisker plot, the first thing we want to do is we want to organize our data set from least to greatest. But the data set is already organized from least to greatest, so we just need to identify a few pieces of information for our box and whisker plots. The first thing we want to identify is our minimum value for the box and whisker, which is the smallest value in our data set. That minimum value is going to be 5. Next, we are going to identify our maximum value, which is the largest value in our data set, and that maximum value is going to be 35. Next, we want to identify our median, and our median is going to be our second quartile for the box and whisker plot. Now, the median is the minimmost value of our data set. Since we are working with the data set of 15, that means the minimost value is going to be the 8th value of the data set, and that is going to give us the median of 20. So our median is going to be 20. Next, we are going to identify our 1st and 3rd quartiles for the box and whisker plot. The first quartile is going to be the median of the lower half of the data set, and that median is going to be 12. So we have a first quartile of 12. The 3rd quartile is going to be the median of the upper half of the data set, and that median is going to be 28. So our 3rd quartile is going to be 28. Now that we have the 1st and 3rd quartile, we can identify the interquartile range. The interquartile range is or is defined as the 3rd quartile minus the 1st quartile. That is going to give us an IQR of 28 minus 12, and we are going to have an interquartile range of 16. Now that we have the interquartile range, let's go ahead and identify our upper and lower bounds of the box and whisker plot. The lower bound is defined as the first quartile minus 1.5 multiplied by the interquartile range. That is going to be 12. -1.5, multiplied by the interquartile range, which is 16. By simplifying, that is going to give us a lower bound of -12. Next, we are going to identify our upper bound for the box and whisker plot. The upper bound is defined as the third quartile plus 1.5, multiplied by our interquartile range. That is going to be 28 plus 1.5, multiplied by 16, and by simplifying, that is going to give us an upper bound of 52. So, now what we need to do is we need to check for any outliers. In order to check for outliers, we want to check and see if our maximum and minimum values are between the upper and lower bounds, which is between -12 and 52. Now, again, our minimum value is 5, and our maximum value is 35. So our 5 and 35 between -12 and 52. Well, the answer to that is yes, so there are not going to be any lower any outliers for our box and whisker plot. Finally, let's go ahead and plot our box and whisker plot by plotting the 1st and 3rd, 2nd quartiles, and the upper and lower bounds, and that is going to give us the following plot. So this is going to be the box and whisker plot that represents the given data set, 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.

2 7 1 3 1 2 8 9 9 2 5 4 7 3 7 5 4
2 3 5 9 5 6 3 9 3 4 9 8 8 2 3 9 5

Key Concepts

Box-and-Whisker Plot

Quartiles

Interquartile Range (IQR)

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