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The data show the maximum wind speeds for a sample of 40 states. Find the mean and modal class for the data.

Class boundaries $\quad$Frequency

$\begin{array}{ll}{47.5-54.5} & {3} \\ {54.5-61.5} & {2} \\ {61.5-68.5} & {9} \\ {68.5-75.5} & {13} \\ {75.5-82.5} & {8} \\ {82.5-89.5} & {3} \\ {89.5-96.5} & {2}\end{array}$

$71.65$ $\\$68.5-75.7

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in this problem. We're looking at data for the max wind speeds for 40 different states on were given all of the class and frequent si for this. And so the very first class is 47.5 to 54.5, and the frequency is three. Um, and then we continue with our classes until we get to 89.5 to 96.5 and then we see the full frequent seed distribution here. I'm so first what we wanted you is add up our total number of frequencies. So we're in and three plus two plus nine plus 13 plus eight plus three plus two to get a total of 40 which we should've already known that it would be 40. But we can just go through the process to double check. So then we need to find the mid point for the class. So if we want to go through the process of finding the midpoint, um, we can take the average so we would do 47.5 plus 54.5 and divided by two to go through the process of finding the midpoint, which for the first class is 51 on. Then we would go through the same process for the second class so we would do 54.5 plus 61.5, divided by two with them or get 58. So as we continue that process on the mid points, we would continue to get would be 65 72 79 86 and 93. So then the next thing we want to do is go through and multiply our frequency by the midpoint. So for this 1st 1 it would be our frequency of three times are midpoint of 51 and we would get 153. And we would do the same thing for the second class, a frequency of two times the midpoint of D eight, and we will get 116. Same thing on the next 19 times 65. Well, the best 585 13 times 72 will be 936. Eight times 79 is 632. Three times 86 is 258. And lastly, two times 93 is 100 86. And then here we also want to find this some, but it's gonna be the summation of our frequency times the midpoint. So the sum of all of these, um so we'll add up 1 53 plus 1 16 plus 585 plus 936 plus 632 posts to 58 plus 1 86 for a total of 2000 866. Then to help us find the mean, um, it's gonna be the summation, uh, which we found. So our summation divided by the number that we have. So, um, are Ennis 40? So, in our case, we're gonna plug in our 2866 which is our summation of our frequency times or midpoint divided by R 40 states. And we will get a mean of 71.65 and then our motile class IHS Um, just the class that happens to have the highest frequency. So our largest frequency and our list here is 13. So that's telling us the motile class is 68.5 to 75.7