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Problem 20 Hard Difficulty

This frequency distribution represents the commission earned (in dollars) by 100 salespeople employed at several branches of a large chain store. Find the mean and modal class for the data.
Class limits $\quad$ Frequency
$\begin{array}{lc}{150-158} & {5} \\ {159-167} & {16} \\ {168-176} & {20} \\ {177-185} & {21} \\ {186-194} & {20} \\ {195-203} & {15} \\ {204-212} & {3}\end{array}$

Answer

177 - 185

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Video Transcript

in this problem. We're looking at data from commissioned earned by 100 sales people. And our first class is 1 50 toe 1 58 with a frequency of five. And then our classes go all the way to 204 to 212. And here is the frequency distribution for the rest of the classes. So the first thing we want to do when we're finding and the mean and the motile class of a group data set is we want to find this some, um, of our frequency column or our in or total number. So we'll add five plus 16 plus 20 plus 21 plus 20 plus 15 plus three for a total of 100 which we should know that we can double check by adding everything. Then we're gonna find the midpoint. So to do that, I'm gonna take, um 1 50 and add 1 58 in our first class and divide it by two on, and that will give us a midpoint of 154. We'll follow the same process for each of the other classes. So for the second class, it would be 1 59 plus 1 67 divided by two to give us a midpoint of 1 63 Then the third midpoint is 1 72 The fourth midpoint ISS 1 81 the next midpoint ISS 190. Then we get a midpoint of 199 and then our last midpoint is 208. So then our last column. We're gonna take our frequency and multiply it by the midpoint. So for this first class, that would be five times a midpoint of 1 54 and the result is 770. We'll keep following the same pattern. So I have 16 times 1 63 gives us 2608 20 times 1 72 will give us 3440 21 times when anyone will give us 3801 20 times when 90 will give us 3800 15 times 1 99 will give us 2985. And lastly, three times 208 will give us 624. So then we want to find the summation of this column. So we're gonna write that as the summation of, um our frequency times the midpoint. And when we at all of these values, we will get 18,000 28. So these two totals will give us, um, what we need to then find the mean. So it's gonna be the summation of our frequency time, Smit Point divided by our total number of values Aymara total frequency. So we'll have 18,000 28 in the numerator divided by 100 and that will give us a mean of 180 0.28. Then for our motile class, we're looking for the highest frequency. So our largest frequency is 21. So that tells us our motile class this 177 to 185.