{1, 3, 5, 7, 9, x, x^2} Which of the following possible values for x

Question

{1, 3, 5, 7, 9, x, x^2}
Which of the following possible values for x would cause the set above to have the largest standard deviation?

A. 5
B. 1
C. 0
D. -1
E. –5

GMATinsight · Answer

P.S. Standard Deviation would Increase if the new value is at a larger deviation from mean than the standard deviation of the set

for given 5 values {1, 3, 5, 7, 9} the mean is 5 hence the value that we must take should be farthest from the mean in order to have the greatest possible standard deviation

Out of the option, x = -5 will be farthest from 5 and also (-5)^2 will be farthest from the mean for x=-5

Answer: Option E

broall · Answer

Make the largest range possible, the answer is E.

mohshu · Answer

mean is 5,,hence pick a value which is remote from 5,,,i.e -5
ans E

JeffTargetTestPrep · Answer

Let’s first calculate the mean of the given 5 numbers:

(1 + 3 + 5 + 7 + 9)/5 = 25/5 = 5

We may recall that the farther away the values in our set are from the mean, the larger the standard deviation. Thus, when selecting a value for x and x^2, we want to select the value that will be farthest away from 5. Let’s test each answer choice.

A) 5

x = 5, x^2 = 25

B) 1

x = 1, x^2 = 1

C) 0

x = 0, x^2 = 0

D) -1

x = -1, x^2 = 1

E) -5

x = -5, x^2 = 25

We see that of our answer choices, x = -5 would produce the largest standard deviation, since both -5 and 25 are farthest from 5.

Answer: E

{1, 3, 5, 7, 9, x, x^2} Which of the following possible values for x

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GMAT Problem Solving (PS) Questions

{1, 3, 5, 7, 9, x, x^2} Which of the following possible values for x

Prep Toolkit

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