Boxplots from Large Data Sets in Appendix B. In Exercises 33–3...

Question

Boxplots from Large Data Sets in Appendix B. In Exercises 33–36, use the given data sets in Appendix B. Use the boxplots to compare the two data sets.

Pulse Rates Use the same scale to construct boxplots for the pulse rates of males and females from Data Set 1 “Body Data” in Appendix B.

Accepted Answer

Hello, everyone, let's take a look at this question together. Using the given data sets, construct a box plot for both groups and compare the two data sets. The table below presents resting heart rates in beats per minute for 10 athletes and 10 non-athletes. Is it answer choice A? Both groups have the same median, but non-athletes have more outliers? Answer choice B, the range of resting heart rates is the same for both groups. Answer choice C, non-athletes have a lower median resting heart rate and a smaller interquartile range, or answer choice D, athletes generally have lower resting heart rates and less variability compared to non-athletes. So the first step in constructing our box plot is to organize the data. So we have our values for the Athletes, and we have the values for the non-athletes, and then we find the 5 number summary for each group. Starting with the athletes, we have our minimum of 48, our Q1 or the first quartile, which is the median of the lower half or the third value of the lower half is equal to 52. Our Q2, or the median is the middle value which the Q2 for the athletes is calculated as 55 plus 57 divided by 2, giving us 56 as the Q2, and our Q3 or the third quartile is the median of the upper half, which is the third value of the upper half. So our Q3 for the athletes is equal to 60, and our maximum value is. 2. Therefore, these are the values for the 5 number summary for the athletes. Then we calculate the five number summary for the non-athletes who have a minimum of 65, a Q1 of 70. AQ2, which is calculated as 74 plus 76, divided by 2, which is equal to 75, and then a Q3 of 80, and a maximum value of 85. So these are the values for the 5 number summary for the non-athletes. Then we need to identify if there are any outliers, starting with calculating the interquartile range. Or IQR, which is calculated as the IQR, is equal to the Q3 value subtracted by the Q1 value. So for athletes, the IQR is calculated as 60, subtracted by 52, which is equal to 8, and for non-athletes, their IQR is equal to 80, subtracted by 70, so the non-athlete's IQR is 10. And then we can check for outliers by computing the lower bound and upper bound values where the lower bound is Q1 subtracted by 1.5, multiplied by the IQR value, and the upper bound is calculated by Q3 plus 1.5 multiplied by IQR, starting with the athletes who have a lower bound value of 40 and An upper bound value of 72, then the non-athletes have a lower bound value of 55, and an upper bound value of 95. And since all the values in both data sets fall within these bounds, there are no outliers. So then the next step is to draw the box plots, which we draw a box from Q1 to Q3 with a horizontal line at Q2. Extend the whiskers from the box to the minimum and maximum values, and since no outliers exist, we do not need to separate the points to be plotted. And then we can compare the distributions, such as the median comparison, where the median heart rate for non-athletes, which is 75 beats per minute, is significantly higher than that of athletes, which is 56 beats per minute. The spread or the IQR, we know the IQR for non-athletes, which was 10 BPM, is larger than that of athletes, which was 8 BPM, indicating slightly more variability in non-athletes, and then for the range, non-athletes have a larger range of 20 beats per minute. Compared to athletes with 14 beats per minute, suggesting that non-athletes have a wider distribution of heart rates. So in conclusion, athletes tend to have lower resting heart rates with less variability, whereas non-athletes exhibit higher resting heart rates with a greater spread. And looking at our answer choices, we can identify answer choice D as the correct answer. As answer choice D, athletes generally have lower resting heart rates and less variability compared to non-athletes. So answer choice D is the only correct answer choice. I hope you found this video to be helpful. Thank you and goodbye.

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Boxplots from Large Data Sets in Appendix B. In Exercises 33–36, use the given data sets in Appendix B. Use the boxplots to compare the two data sets.

Pulse Rates Use the same scale to construct boxplots for the pulse rates of males and females from Data Set 1 “Body Data” in Appendix B.

Key Concepts

Boxplots

Quartiles

Comparative Analysis

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Boxplots from Large Data Sets in Appendix B. In Exercises 33–36, use the given data sets in Appendix B. Use the boxplots to compare the two data sets.Pulse Rates Use the same scale to construct boxplots for the pulse rates of males and females from Data Set 1 “Body Data” in Appendix B.