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If variance of x is 24, then what is the variance of (x+1)/2?

A)24 B)12.5 C)24.5 D)6 E)8

It seems tough since you don't have the data. If you have the data, you could add 1 to each of them then divide by 2. Now you don't have them

(24+1)/2=12.5 ? WRONG

Rules: 1-Variance of X if added or subtracted by a number, remains the same 2- Variance of X if multiplied or divided by a number, is multiplied or divided by that number squared.

So, let's write (x+1)/2 in this way: x/2 + 1/2

considering rule #1, we omit the second part, 1/2. So, now we wanna calculate the variance for x/2. As rule #2 say, we should divide 24 by 4 (2 squared)

solution= 6

Source: my own question. I know it's not a standard GMAT question, but who knows, maybe GMAC decides to continue ever growing difficulty of GMAT by including these easy rules

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Lets assume data set of numbers {2,4,6} The mean is 4. Variance of {2,4,6} = [(2-4)^2 + (4-4)^2 + (6-4)^2]/3 = (4 + 0 + 4)/3 = 8/3

Now lets translate the values {2,4,6} to {3,5,7} The mean is 5. Variance does not change Conclusion : Variance does not change on adding one to each number

Now lets divide each one by 2. Hence the set becomes {1,2,3}. The mean is 2 The variance is [(1-2)^2 + (2-2)^2 + (3-2)^2] / 3 = (1 + 0 + 1)/3 = 2/3 Conclusion : The variance gets divided by 2^2 when each number gets divided by 2.

If variance of x is 24, then what is the variance of (x+1)/2 -- The answer is 24/2^2 = 24/4 = 6

1-SD of X if added or subtracted by a number, remains the same 2- SD of X if multiplied or divided by a number, is multiplied or divided by that number