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.

Systolic Blood Pressure Use the systolic blood pressures of the 300 subjects included in Data Set 1 “Body Data.” Use a class width of 20 mm Hg and begin with a lower class limit of 80 mm Hg. Does the frequency distribution appear to be a normal distribution?

Accepted Answer

Welcome back everyone. In this problem, a health study recorded the diastolic blood pressure, or DBP readings of 50 patients. Construct a frequency distribution using a class width of 10 millimeters of mercury, starting with a lower class limit of 50 millimeters of mercury. Does the frequency distribution suggest a normal distribution? And here are the different uh millimeter, the different DBP readings for each patient. Now notice in our problem, we were told that we should construct our distribution with a class width of 10 millimeters of mercury, starting with a lower class limit of 50 millimeters of mercury. So let's make a new table, OK? And let's have our class intervals. And we know if we're constructing a frequency, OK. Then we're going to find the frequency of each, OK? So this is in millimeters of mercury. And then we're gonna have our frequency F. OK. I know, like we said. The first class starts at 50 millimeters of mercury and increases by 10 each time. So you're gonna have a class from 50 to 59, then 60 to 69. 70 to 79. 802 89. 90 to 99. And then 100 to 109. Because if we were to look at the values in our table, OK, we can tell here that 100 is the highest value. Now, all we need to do is to count how many values file in each class and then use that to construct our frequency table, OK? So let's go ahead and do that. First, let me put this properly here. First, let's start with our interval 50 to 59. How many values fall between 50 to 59? Well, if we start to count, we have 52. 59 and on our in our second row uh we continue counting here there's none that falls between 50 to 59 in our third row 54, 55 in our fourth row we have 56 and then in our 6th row we have 58, 57, and 53. So how many values are those? 12345678. Therefore, the frequency for our class interval from 50 to 59 is 8. Now, to find the frequency for the rest of classes, essentially we do the same thing. So I'll allow you to spend time on those as well, but you should find that for the interval from 60 to 69, the frequency is 10. For the intervals 70 to 79, the frequency is 12. For 80 to 89. It should be 13, OK. From 90 to 99, you should get 6, OK. And then from 100 to 109, you should find that you get 1, OK? So these are the class intervals and their frequencies. Now remember, the next part of our problem says if the frequent or sorry, if the frequency distribution suggests a normal distribution, what do we know about normality? Well, we know that it's symmetric and it will also be follow a normal distribution if it resembles a bell pattern. Now, first, to check for symmetry, we want to see if our frequencies increase as the classes get larger and then decrease the larger they get, OK, because essentially that means if for for a normal distribution we know that this is how it would look. It's symmetric on both sides. Now notice here starting from 50 to 59, it goes from 8, then to 10, then to 12 and 13 in the middle of the distribution, and then from 90 to 99 it's 6, from 100 to 109, it's 1. So this tells us then that our distribution is symmetric because the frequencies increase, peak around 80 to 89, and then decrease. Also, if we check the pattern, the distribution resembles a bell pattern if it follows that type of symmetry. Thus it suggests a roughly normal distribution. Therefore, the distribution, OK, the distribution we could write that the distribution is. An approximate normal distribution. Even though slight deviations may exist, we know it's not a perfect normal distribution, but based on the values we can tell that it could be approximate. Thanks for watching everyone. I hope this video helped.

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Key Concepts

Frequency Distribution

Class Width

Normal Distribution

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