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

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

Hi everyone, let's take a look at this practice problem. This problem says you find the five number summary of the data set, and we're given the data of 21, 25, 23, 22, 24, 26, 28, 29, 27, 25, 24, 23, 22, 21, 23, 24, 25, 26, 27, 28, 29, 30, 28, 27, 26, 25, and 24. So, in order to find our 5 number summary, the first thing we need to do is to order our data in ascending order. So, starting with the smallest value, we will have 21. The 21 again. And 22. Then 22 again. Then 23. Then 23 again. The 23 for a third time. Then 24. 24 for a second time. 24 for the 3rd time. 24 for a 4th time, and 24 for a 5th time. And then we'll have 25. 25 again. 25 for a third time. And 25 for a 4th time. Then we'll have 26. 26 again. 26 for a third time. Then 27. 27 again. 27 for a third time. Then 28. 28 again. 28 for a third time. Then 29 And finally, 30. So now that we have our data set ordered, we can read off the minimum and maximum values. So, for the minimum value, That is going to be equal to. 21. And our maximum value is going to be equal to 30. So those are two of our 5 number summary values that we're looking for. Next, we'll calculate the median. Which is Q2. And recall that the median is the value that appears in the middle of our data set, once we have ordered our data set. Since we have 27 values, the value in the middle is going to correspond to the 14th value. Which, when we look at our head, is actually 25. That means that Q2 is going to be equal to 25, and that is another one of our 5 number summaries, calculated. Next, we need to calculate our 1st and 3rd quartiles. So, we'll start off with the 1st quartile, Q1. Recall that that is going to be the median of the data that is below the median. So, here we're looking at the 1st 13 values. Of our data. So, the median of this data set is going to be the 7th value, which turns out to be 23. So that means that Q1 is going to be equal to 23. That is another of our 5 number summaries calculated. And the final value that we need to find is going to be Q3. Which is our 3rd quartile, and that recall that that is the median of the upper half of our data. So that is going to be the median of the final. 13 data points in our data set. So, here, since we have 13 data points, we're gonna be looking for the 7th value. And that actually corresponds to 27. So that means that Q3 is equal to 27. So that is the final value of our five number summary. So our final answer is going to be the minimum equal to 21, Q1 equal to 23, Q2 equal to 25, Q3 equal to 27, and our maximum equal to 30. So that is the answer that this problem was looking for. 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

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

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 summary2 7 1 3 1 2 8 9 9 2 5 4 7 3 7 5 42 3 5 9 5 6 3 9 3 4 9 8 8 2 3 9 5