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# Solve this 820 level variance question :)

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Manager
Affiliations: University of Tehran
Joined: 06 Feb 2011
Posts: 203
Location: Iran (Islamic Republic of)
Concentration: Marketing
Schools: Wharton
GMAT 1: 680 Q45 V38
GPA: 4
WE: Marketing (Retail)
Solve this 820 level variance question :) [#permalink]

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10 Apr 2011, 11:24
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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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Re: Solve this 820 level variance question :) [#permalink]

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10 Apr 2011, 11:43
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
Manager
Affiliations: University of Tehran
Joined: 06 Feb 2011
Posts: 203
Location: Iran (Islamic Republic of)
Concentration: Marketing
Schools: Wharton
GMAT 1: 680 Q45 V38
GPA: 4
WE: Marketing (Retail)
Re: Solve this 820 level variance question :) [#permalink]

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10 Apr 2011, 11:49
hmm. You just proved the rules, good.

Now, please write the same rules for deviation. I'll come back later
_________________

Ambition, Motivation and Determination: the three "tion"s that lead to PERFECTION.

World! Respect Iran and Iranians as they respect you! Leave the governments with their own.

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
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Re: Solve this 820 level variance question :) [#permalink]

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10 Apr 2011, 11:59
Rules are the same with a twist in 2)

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
Manager
Affiliations: University of Tehran
Joined: 06 Feb 2011
Posts: 203
Location: Iran (Islamic Republic of)
Concentration: Marketing
Schools: Wharton
GMAT 1: 680 Q45 V38
GPA: 4
WE: Marketing (Retail)
Re: Solve this 820 level variance question :) [#permalink]

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10 Apr 2011, 12:27
uh uh, good, but you made a mistake about the second rule: divided or multiplied by the absolute value of that number. It makes a change.
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Ambition, Motivation and Determination: the three "tion"s that lead to PERFECTION.

World! Respect Iran and Iranians as they respect you! Leave the governments with their own.

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Status: There is always something new !!
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Joined: 08 May 2009
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Re: Solve this 820 level variance question :) [#permalink]

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18 May 2011, 03:45
good rule for variance.

However using SD^2 = variance

SD for x = 4.8 approx
SD for (x+1)/2 = 2.4 approx

variance for new set = 2.4^2 = 5.76 = approx 6.

Hence D
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Re: Solve this 820 level variance question :)   [#permalink] 18 May 2011, 03:45
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