Set J consists of the terms {a, b, c, d, e}, where e > d

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Oct 12, 2015 10:58 pm

Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 1. Which of the following operations would decrease the standard deviation of Set J?

A. Multiply each term by e/d
B. Divide each term by b/c
C. Multiply each term by âˆ’1
D. Divide each term by d/e
E. Multiply each term by c/e

Answer: Option E

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Source: Beat The GMAT — Problem Solving | Mon Oct 12, 2015 10:58 pm

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Oct 12, 2015 10:58 pm

GMATinsight wrote:Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 1. Which of the following operations would decrease the standard deviation of Set J?

A. Multiply each term by e/d
B. Divide each term by b/c
C. Multiply each term by âˆ’1
D. Divide each term by d/e
E. Multiply each term by c/e

Answer: Option E

CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number

A. Multiply each term by e/d is equivalent to multiplying each term with some value>1 which will Increase the SD

B. Divide each term by b/c is equivalent to Dividing each term with some value<1 which will Increase the SD because b/c<1

C. Multiply each term by âˆ’1 will keep the deviation of the terms same only the signs of the terms in set will change hence, No change in SD

D. Divide each term by d/e is equivalent to Dividing each term with some value<1 which will Increase the SD because d/e<1

E. Multiply each term by c/e is equivalent to multiplying each term with some value<1 which will DECREASE the SD by the coefficient c/e

Answer: option E

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