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

Question

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

(a) find the five-number summary

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

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says do you find the five number summary of the following data set 1215, 1114, 1317, 1612, 1815, 1413, 1916, 1517, 1312, 18, and 14. So we're asked to find the 5 number summary, so the first thing we need to do is to order our data set in the ascending order. In doing so, we will get 11. 12 12 again Well, for a 3rd time, 13 13 again. 13 for a 3rd time. Then we'll have 14. 14 again. 14 for a 3rd time. Then 15? 15 again. 15 for a 3rd time. 16? 16 again. 17. 17 again. 18 18 for a second time. And 19. So now that we have our data ordered, we can actually read off our minimum and maximum values. For the minimum value, that is going to be equal to 11. And the maximum value is going to be equal to 19. So those are two of our 5 number summaries already found. Next, we need to find our medium. Which is denuded you too. They recall that our median is the value that is in the middle of our ordered sequence here. Since we have an even number of data points, since we have 20 data points, We're actually gonna be looking at the midpoint between the two values that appear in the middle, and the two values that show up in the middle are 14 and 15, so that's the 10th and 11th. Values So that means that Q2 is going to be equal to, and here we have to recall how to calculate midpoints, so we'll add our two values together, so we'll have 14 plus 15, and we'll divide that quantity by 2. That means that Q2 is going to be equal to 14.5. So that is our 3rd value of our 5 number summary found. Next, we're going to need to calculate our first quartile and 3rd quartile values. We'll start off with our first quartile value, Q1. I recall that Q1 here is going to be the median, median of the lower half of our data, so between 11 and 14. So here we're looking for the median of our 10 data points, and again, we have an even number of data points. So we're gonna look at the midpoint between the two values in the middle. So that is going to be between the 5th and the 6th values in our sequence here, and that is 13 and 13. Now, since these two are the same, we don't really need to find the midpoint, that just means that Q1 is going to be equal to 13. So that is another one of our 5 number summaries found. And the final value that we need to find is our third quartile, Q3, and recall that that is going to be equal to the median of the upper half of our data, so between 15 and 19. Again, we have 10 data points here. So since we have an even number of data points, we'll look at the midpoint of the two values in the middle, which is going to be the midpoint between 16 and 17. So that means that Q3 is going to be equal to the quantity of 16 plus 17 in quantity, divided by 2, and this is going to be equal to. 16.5. So that is the final value that we need to find for a 5 number summary. So, just to recap, we have a minimum value of 11. Q1 is equal to 13, Q2 is equal to 14.5, Q3 is equal to 16.5, and our maximum value is 19. So those are going to be the answers for this problem. So I hope that this explanation has been useful, and I'll see you in the next video.

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Drawing a Box-and-Whisker Plot In Exercises 15–18,
(a) find the five-number summary

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

Key Concepts

Five-Number Summary

Box-and-Whisker Plot

Quartiles

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Drawing a Box-and-Whisker Plot In Exercises 15–18,(a) find the five-number summary4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9