## mean of 8 numbers is 3, mean of 12 is x, mean of all is 9

Standard deviation, mean, variance, z-scores, t-tests, etc.
maggiemagnet
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### mean of 8 numbers is 3, mean of 12 is x, mean of all is 9

In the assignment, they wrote:The mean of a set of eight numbers is 3 and the mean of a different set of twelve numbers is x. Given that the mean of the combined set of twenty numbers is 9, calculate x.

My thinking: Since the average of the 8 numbers is 3, and you find this average by dividing the total by 8, then that total is 8*3 = 24, right? So would the total of the others be 12*x, with the combined total being 20*9 = 180? And then you add the two smallers numbers and make this equal to the combined total?

stapel_eliz
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maggiemagnet wrote:My thinking: Since the average of the 8 numbers is 3, and you find this average by dividing the total by 8, then that total is 8*3 = 24, right? So would the total of the others be 12*x, with the combined total being 20*9 = 180? And then you add the two smallers numbers and make this equal to the combined total?

You're exactly right: the "trick" to this sort of exercise is to neglect the averages, and multiply (that is, work backwards, using the definition) to find the total that created that average. You have the right set-up, too:

. . . . .$24\, +\, 12x\, =\,180$

Isolate the term with the $x$:

. . . . .$12x\, =\, 180\, - \, 24$

...and divide through to find the average of the second set of numbers.

Eliz.

maggiemagnet
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Joined: Mon Dec 08, 2008 12:32 am
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Thank you!