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Find the mean for the following.

$\begin{array}{cc}{\text { Value }} & {\text { Frequency }} \\ \hline 9 & {3} \\ \hline 12 & {5} \\ \hline 15 & {1} \\ {18} & {1}\end{array}$

12

Multivariable Optimization

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this question gives you a frequency table and asks you to find the mean of the date of its describing in this table the values which I'll call X or equal to nine, 12 15 and 18. Um, the frequencies, which are called F, are equal to 43 There's three nines, five twelves 1 15 and 1 18 Now we know that finding frequency are finding that mean X bar from a frequency table like this. We need to find the sum of all the of all the values times the frequencies over n and end is equal to the sum of all the frequencies. So let's ah, first, I'm gonna make it column Another column In this frequency table, it's X times F um, we'll have nine times three, which is 27 12 times five, which is 60 and and 15 times 1 15 and 18 times 1 18 So these are all the values for X times f. And now what I want to do is at a row on the bottom where we add all of them up. This will be the total row. We don't really care about Thea. Some of the values that doesn't help us find the mean. Um, but we do want to know that some of the frequencies here three plus five plus one plus one that's gonna be 10 and some of the X times f values. If we add all those up, we're gonna get 120. So remember the sum of F. What we found here is the same thing is end. So now we know that n is equal to 10 and the sum of X times F is equal to 1 20 So when we plugged it into our mean equation will get that X bar Zagato 1 20/10 or just 12 and that's your