use the frequency distribution to find the (a) class width, (b...

Question

use the frequency distribution to find the (a) class width, (b) class midpoints, and (c) class boundaries.

Toledo, OH, Average Normal Temperatures (F)

Table displaying frequency distribution of average normal temperatures in Toledo, OH, with class intervals and corresponding frequencies.

Accepted Answer

Welcome back, everyone. A frequency distribution for the weight in kilograms of a group of students is given below. What is the class width? What are the class midpoints, and what are the class boundaries? Now here we're given the class intervals and the frequencies. So let's start by trying to figure out the class width. Recall OK, that the class with. Is equal to the low the upper limit, OK, of any class, OK. Minus the lower limit of any class. Plus 1, OK? So we can use any class to determine the class width. I know we again as we said, we can choose any. So let's say that we were using the first class from 45 to 54, OK. Then our class width. Is going to be equal to 54, the upper limit minus 45, the lower limit plus 1. 54 minus 45 is 9 and the 9 + 1 equals 10. Therefore, our class width is 10. Next, let's try to figure out the class midpoints. What do we know? Well, recall again that the class midpoint. OK, it's the value that's halfway through the class. In other words, it's equal to the lower limit. Plus the upper limit, OK. Divided by 2. So to find a class mid midpoint for each class, let's add their limits and then divide by 2. So, for example, for the class 45 to 54, it's midpoint, OK, is going to be equal to 45 plus 54 divided by 2. And that would be equal to 49.5. Next, for 55 to 64, that's going to be equal to 55 plus 64 divided by 2, which would be equal to 59.5. Next, uh, we have 65 to 74. So that's 65 plus 74 divided by 2, which equals 69.5. Then we have 75 to 84. So that's 75 plus 84 divided by 2, which is 79.5, OK. And then finally we're going to have, well, you know what, I think I should. I think I should probably make some space to the right here. We, because we still have a third part of the problem to do. So for the class 85 to 94, it's midpoint is 85 + 94 divided by 2, which is 89.5. Thus, these are all of the class midpoints for our class intervals. Now let's move on to the 3rd part of our problem. What are the class bones? OK. Well, the class bounds are found by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class to eliminate gaps. So in this case, For 45 to 54, it's class limit, it's class bungee, it's lower class bungee, sorry, would be 45 minus 0.5, which is 44.5, and it's upper class bongi would be 54 plus 0.5, which is 54.5. Next, uh, for 55 to 64, OK, it bones are gonna be 54.5 to 64.5, OK. Then for uh 65 to 74, those boundaries will be. Uh, 64.5 to 74.5. For 75 to 84, it's 74.5. So, well, I should, I was using the hour before, so let's just keep this consistent. So, 74.5 to 84.5, and then for 85 to 94, it's going to be 84.5. 294.5 Thus these are the class boundaries for our class intervals. Thanks a lot for watching everyone. I hope this video helped.

use the frequency distribution to find the (a) class width, (b) class midpoints, and (c) class boundaries.
Toledo, OH, Average Normal Temperatures (F)

Key Concepts

Class Width

Class Midpoint

Class Boundaries

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