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Problem 14 Medium Difficulty

The hourly compensation costs (in U.S. dollars) for production workers in selected countries are represented below. Find the mean and modal class for the data.
Class$\quad$ Frequency
$\begin{aligned} 2.48-7.48 & & & 7 \\ 7.49-12.49 & & 3 \\ 12.50-17.50 & & 1 \\ 17.51-22.51 & & 7 \\ 22.52-27.52 & & 5 \\ 27.53-32.53 & & 5 \end{aligned}$

Answer

17.148 $\\$2.46-7.48 $\\$17.51-2.2.51

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Video Transcript

in this problem. We're looking at a data set for the hourly wage for production workers in U. S. Dollars. Um, our very first class is 2.48 to 7.48 and it has a frequency of seven. Um, then we'll continue to the second class, and it will pick up right where we left off with 7.49 to 12.49. Here's the rest of the classes as well as their frequencies. And one of the very first things you want to do is add up our total number of frequencies to get our end. So we'll have seven plus three plus one plus seven plus five plus five for a total of 28. Then we want to find the midpoint. So to calculate the midpoint, we're going to do to 0.48 lest 7.48 and divine that by to. And once we do that for this first class, the midpoint is going to be four point 48 and then we'll continue that same process of adding the lowest and the highest numbers in the class and dividing by two to find the midpoint so we will get 9.99 Then we will have 15. Following that same process, we get 20.1 then 25.2 and 30 0.3 Then for this other column The last column. We're gonna do the frequency times the midpoint. So for this first class, that's gonna end up being our frequency of seven times the midpoint of 4.48 and on the result of that is 34.86. Then we'll do the same thing three times. 99 will give us 29.97. One times 15 is, of course, 15 seven times 20.1 is 1 40 0.7 Five times 25.2 is 1 25.1 and five times 30.3 is 1 15 0.15. And then here I'm similar to when we added up their frequencies. We wanna add up, Um, our multiplication here. So this is gonna be this summation of our frequency times our midpoint, and we will get a total of 480.15 for this column. So then these two numbers The summation of, um, are multiplication ins and the summation of our frequencies are gonna be what we use them to find our mean, still remain equals the summation of our frequency. Times are midpoint, so we know that's 480 0.15 divided by the total number of frequencies that we had, which we found with 28. And we will get a mean of 17.1 48 where that would round to 17 dollars and 15 cents. Then for our motile class, we're looking for the class that has the highest frequent scene. I'm so for this status that we have the highest frequency is seven, and that's happening twice. And so we actually have to motile classes to 0.48 to 7.48 as well as 17.15 1 to 22.51