In Exercises 5 and 6, construct the dotplot.

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Question

In Exercises 5 and 6, construct the dotplot.

Diastolic Blood Pressure Listed below are diastolic blood pressure measurements (mm Hg) of females selected from Data Set 1 “Body Data” in Appendix B. All of the values are even numbers. Are there any outliers? If so, identify their values.

Diastolic blood pressure measurements in mm Hg, all even numbers, displayed in a horizontal list format.

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a sports scientist records the resting respiratory rates, breaths per minute of a group of athletes. The recorded values are given below and we're given the values of 1214, 1618, 2020, 2022, 24, 24, 24, 26, 26, 26, 28, 28, 30, 30, 32, 34, 36, and 36. We're also asked to construct a dot plot for the given data, and we're asked the question, are there any outliers? If so, identify their values. Well, the problem we're given a graph on which to create our dot plot. So the first part of this problem, we want to construct a dot plot for a given data. And normally to construct a dot plot, you'll first want to order your data from the smallest value to the largest value. However, our data is already in that order. So now what we're going to do is just place a dot at the given value for the number of times that it appears. So if it appears once, we'll have 1 dot. If it appears 2 times, we'll have 2 dots, and so forth. So, for our first data point, we have 12, and it shows up once, so we'll place 1 dot. Above 12 The next value is 14. It also appears once, so we'll just place a single dot above 14. For 16, the next data point, it also just appears once, we'll place a single dot. For 18, it also just appears once, we'll place a single dot. For 20, it appears 3 times, we'll actually place 3 dots above 20. Next value is 22, it occurs once in our sequence, and so that It's just going to have a single dot above it. The next value is 24, it appears 3 times, so we will have 3 dots above 24. The next value is 26, and it also appears 3 times, we'll place 3 dots above 26. The next value is 28, and it appears twice, so we'll have two dots above 28. The next value is 30, and it appears twice, so we'll have two dots above 30. The next value is 32, it appears once, so we'll just have a single dot. The next value is 34. It also just appears once, so we will have a single dot above 34, and the final value is 36, and it appears twice, we'll have two dots. Above 36. So, the graph that we have created here is the answer for the first part of our question. Now, for the second part, we need to identify any outliers. And for this, we're going to use the interquartile range. So, in order to determine the interquartile range, we first need to calculate our 1st quartile and 3rd quartile. So, for the 1st quartile, we're going to be looking at the median. Of the 1st 11 points, which is just the first half of our data. So, if I look at the median value, That appears to be 20, if we look at our data. So that is the 6th value in that sequence. So that means that Q1, which is our first quartile, is going to be equal to 20. Now, to find the 3rd quartile, we'll find the median of the last half of our data, so the last 11 points. So, again, that's going to be the 6th data point in the sequence, and that turns out to be 30. So that means our 3rd quartile, Q3, is going to be equal to 30. So now we need to calculate our interquartile range, which will abbreviate as IQR. And recall that this is going to be equal to Q3 minus 21. Which is equal to 30 minus 20. And that is equal to 10, we evaluate that expression. So now we have the interquartile range, we can calculate our lower bounds and upper bounds. So for our lower bound, which will abbreviate as LB. That's going to be equal to, if you recall, Q1 minus 1.5, multiplied by our interquartile range IQR. And this is going to be equal to 20 minus 1.5, multiplied by 10. Which is equal to 5 when we evaluate that expression. Now, for the upper bound, recall that that is going to be equal to Q3 plus 1.5, multiplied by our interquartile range IQR. And this is going to be equal to 30. Plus, 1.5, multiplied by 10. And evaluating the expression that it's going to be equal to 45. So any outlier is going to fall outside of the interval from 5 to 45. However, if we look at our data, we see that all the values fall between 12 and 36. So all of our data points do fall within our lower bound and upper bound. So, since all of our data falls between our lower bound and upper bound, that means that we have no outliers. That is going to be the answer for the second half of this problem. So, I hope that this explanation has been useful, and I'll see you in the next video.

In Exercises 5 and 6, construct the dotplot.

Diastolic Blood Pressure Listed below are diastolic blood pressure measurements (mm Hg) of females selected from Data Set 1 “Body Data” in Appendix B. All of the values are even numbers. Are there any outliers? If so, identify their values.

Key Concepts

Dotplot

Outliers

Diastolic Blood Pressure

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