In Exercises 5–8, identify the class width, class midpoints, a...

Question

In Exercises 5–8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B.
7.

7. Table displaying blood platelet count ranges for males alongside their corresponding frequencies.

Accepted Answer

All right, hello, everyone. So this question says heart rate measurements. The table below summarizes the resting heart rate and beats per minute of a group of individuals. Identify the class with, class midpoints, and class boundaries for the given frequency distribution. Also, determine the total number of individuals included in the summary. And here we have the data shown with resting heart rate and beats permitted on the left and the frequency for each category on the right. All right, so here, if I scroll down very quickly, you can see that I've already made a table with all the information needed for the question. That is, I have 4 columns in total, one that says classes, another class width, the midpoints, and the class boundaries. Now, the classes themselves are the ranges of heart rates and beats per minute that were provided in the data table, so I just copied those. Now let's begin by finding the class width. Now the class width, if you recall, is found by subtracting the lower boundary of one class from the lower boundary of the next class. So when considering the first two classes, for example, the lower limit of the first is 40 and the lower limit of the second is 80. So the difference between those would be the class width, which in this case happens to be 40. And for each class, the width just so happens to be 40, so I'm just going to write that out. Now, the class midpoint, on the other hand, is found using the above formula, and let me actually scroll up to open some space here. The midpoint, or MP for short, is equal to the lower bound of a given class. Added to the upper bound and divided by 2. So it's the sum of the upper bound and lower bound of one class divided by 2. So giving an example or using the first class as an example, the lower limit is 40, the upper limit is 79. So the midpoint is equal to the sum of 40 and 79 divided by 2, which just so happens to be 59.5. And so the calculation would be the same for all of the remaining classes. For the second class, the midpoint is 99.5. For the third it's 139.5. For the 4th it's 179.5. For the 5th It is 259.5. And for the 6, it is 299.5. And then for the 6th category, the midpoint, or the 6th class, rather, the midpoint is. I do apologize for the abrupt cut, but I just wanted to make a very quick correction. There was one class that I actually skipped when talking about the midpoint calculations. Specifically, I had skipped the class between 200 and 239 beats per minute. That has a midpoint of 219.5. So I just wanted to include that in the data set. So now, our last step is to find the class boundaries. And so for the class boundaries, what they do is ensure that there are no gaps between consecutive intervals. So here, For a given class, to find the lower boundary, you're going to take the lower limit of that class and subtract 0.5. For the upper boundary, you take the upper limit of the given class and add 0.5. So using the first class as an example from 40 to 79. You would subtract 0.5 from 40 to give you 39.5. And then you would add 0.5 to 79 to give 79.5. And then for all the remaining classes, you would do the same. So for the 2nd interval, Your boundaries would be from 79.5 to 119.5. For the third class it would be 119.5. Added to 159.5. For the 4th, it would be 159.5. Added to 199.5. For the 5th, it would be. 199.5 up to. 239.5. For the 6th class, it would be. 239.5 up to 279.5. And for the last class, it would be from 279.5 up to 319.5. So this completes the data table. So now our final step is to find The total number of individuals included in this data set. And so to find the total number of individuals, what you do. I go back to the original data set and add all the frequencies together of each class. So, you would find the sum of 2, 48, 85, 15, 00, and 2. And that number comes out to 152. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.