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Find the mean for the following.

$\begin{array}{ll}{\text { Value }} & {\text { Frequency }} \\ \hline 4 & {6} \\ \hline 6 & {1} \\ \hline 9 & {3} \\ \hline 15 & {2}\end{array}$

7.25

Multivariable Optimization

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Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

this question gives you a frequency table and asks you to find the mean of the data the values which all right as x R 469 and 15. And in the frequencies, which all right, it's f of each of those values Air six there, six fours, 163 nines and to fifteens. Now we know from our textbook that the way we find the meaning X bar is gonna be the sum of X times f for each for each data point divided by N and now N is the total number of minutes. It's the sample size, the total number of data points. And that's the same as the sum of F. So I'm gonna write that instead. We'll have that. So what I'm gonna do here at the bottom of the well, first, I'm gonna find X times fr at a column toe a frequency table that that is X times F. So we'll go ahead through each row. Four times six is 24 6 times one is 69 times three is 27 15 times two is 30. No, at a, uh, row at the bottom for the some that we're gonna add up our x Times F column for numerator and r F Column for a denominator and see what we get money out of our F column. Six plus one plus three plus to get 12. So the sum of F is 12 and then we add up our X Times F column. We get 24 plus six was 27 plus 30 and that is 87. So now we know that the sum of X Times F is equal to 87 the some of, uh, f is just able to 12. So that means explore is going to be equal to 87/12 which is equal to 7.25 and that is your final answer.