Exercises 29–34 involve large sets of data, so technology shou...

Question

Exercises 29–34 involve large sets of data, so technology should be used. Complete lists of the data are not listed in Appendix B, but they can be downloaded from the website TriolaStats.com. Use the indicated data and construct the frequency distribution.

Diastolic Blood Pressure Use the diastolic blood pressures of the 300 subjects included in Data Set 1 “Body Data.” Use a class width of 15 mm Hg and begin with a lower class limit of 40 mm Hg. Does the frequency distribution appear to be a normal distribution?

Accepted Answer

Welcome back everyone. In this problem, a university health center recorded the resting heart rates or beats per minute BPM of 50 students during a wellness checkup. Construct a frequency distribution using a class width of 5 BPM, starting with a lower class limit of 55 BPM. Does the frequency distribution suggest a normal distribution? And here we have our resting heart rates for the 50 students. Now notice that our problem told us that we need to construct the distribution using a class width of 5 BPM and start with a lower class limit of 55 BPM. So let's make a table of class intervals. So we have the intervals. And we have their frequencies. And now, if I were to put this as a table here. And like our problem says, starting at 55, we give a class with 5 BPM, so we're gonna have 55 to 59. 60 to 6465 to 69. 70 to 74. 75 to 79. 80 to 84, OK, probably need some more space here. 85 to 89. 90 to 94 and then 95 to 99 and 95 to 99 is going to be our last class because if we look in our data set, 95 is the highest value. So this is, or these are our class intervals. To find the frequency of each class interval, we can count how many data points fall into each range and write them as their frequency. So for example, in the interval of 55 to 59, how many values in our data set fall in that range? Well, from our first row we have 56. From the second row there would be no values. From the third row there would be one value 57. From the 4th row, we'd have uh 59, OK? And from the 5th row, we would have 55 and 58. So, that's 12345. Therefore, the frequency of the class interval of 55 to 59 is 5. Essentially, we're just going to repeat the same process for the rest of the intervals. And I'll leave that to you to complete or to do, but you should find that for the intervals 60 to 64, we have 6 data points. 65 to 69 is 6 data points, 70 to 74 is 6 data points. 75 to 79 is 9 data points. 80 to 84 has 6. 85 to 895. 90 to 94 has 6, and then 95 to 99 has 1. OK? So this is a table of our class intervals and their frequencies for the 50 resting heart rate values. No, we can test the second part of our problem statement. Does this represent or does this suggest a normal distribution? How can we know that? Well, recall that in a normal distribution, OK, it has a bell-shaped pattern which is symmetric, OK? So the values increase, reach a maximum, and then they start to decrease. So if we can observe that pattern within our data set, that means it suggests a normal distribution. So if we were to imagine this. OK. On a graph, or imagine these points on a graph, if we think about it here, starting with our first value, we have 5, then 666, and then 9, OK? And then it goes back to 6, goes to 5, goes to 6, and then goes to 1. So it's not a perfect normal distribution, but generally here we can tell that the frequencies increase, peak around 75 to 79 BPM, and then decrease. So that means the distribution the data suggests an approximate normal distribution. So let's write that. The data suggests. An approximate. Norma Distribution. Even though slight deviations as we can tell here will exist. Therefore, this is our frequency table and it suggests an approximate normal distribution. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Frequency Distribution

Class Width

Normal Distribution

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