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Set A consists of all even integers between 2 and 100 [#permalink]
14 Mar 2011, 08:20

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Set A consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set A by 50, set Y is derived by multiplying each term in set A by 1.5, and set Z is derived by dividing each term in set A by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?

(A) X, Y, Z (B) X, Z, Y (C) Y, Z, X (D) Y, X, Z (E) Z, Y, X

Set A consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set A by 50, set Y is derived by multiplying each term in set A by 1.5, and set Z is derived by dividing each term in set A by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation? (A) X, Y, Z (B) X, Z, Y (C) Y, Z, X (D) Y, X, Z (E) Z, Y, X

pls explain the concept too....?? how do we find the spread frm mean when there r many terms involved..??

Set A - {2, 4, ..., 100}; Set X - {-48, -46, ..., 50}; Set Y - {3, 6, ..., 150}; Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.

If we add or subtract a constant to each term in a set the SD will not change, so sets A and X will have the same SD.

If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set A and set Z will have 4 times less SD than set A (note SD can not be negative so SD of Z wil be SD of A divided by 4 not by -4).

So, the ranking of SD's in descending order is: Y, A=X, Z.

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

You can see that set Y is most widespread and set Z is least widespread, so the correct answer is: Y, A=X, Z.

Re: Set A consists of all even integers between 2 and 100 [#permalink]
09 Aug 2014, 20:00

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