Mean of n numbers is p .... Multiple Choice Question

Dr.Peterson

Elite Member
View attachment 28867Answer is A but I am unsure how to tackle this question.

I wrote the mathematical expressions for each sentence but I am unsure where to go from there.
Please show those expressions, so we can know where you are! Then also tell us what ideas you have for the next step.

Jomo

Elite Member
Let the n numbers be a1, a2, a3, ...., an.
Then the average would be (a1+a2+...+an)/n = p

The mean of a1 and a2 is q. That is (a1+a2)/2 = q. So how much is a1+a2

The remaining numbers have a mean of (a3+a4+...+an)/(n-2) = 10. How much is a3+a4+...+an?

Continue from here. 1st find out what a1+a2+...an equals in terms of n, p and q.

HallsofIvy

Elite Member
I hope you understand that the "mean" of n numbers is the sum of those number divided by n so that the sum of the numbers is n times that mean.

If "the mean of n numbers is p" then the sum of the n numbers is np. If the mean of two numbers is q then the sum of those two numbers is 2q. If the mean of the remaining n- 2 numbers is 10 then the sum of those remaining numbers is 10(n-2).

Of course, the sum of those two numbers and the remaining n-2 number is the sum of all n numbers: np= 2q+ 10(n- 2).

np= 2q+ 10n- 20

np- 10n= 2q- 20
n(p- 10)= 2q- 20
$$\displaystyle n= \frac{2q- 20}{p- 10}$$

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