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Set B has 7 members and x and y are distinct positive integers. If x
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29 Mar 2017, 03:55

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E

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65% (hard)

Question Stats:

60% (01:40) correct 40% (02:09) wrong based on 94 sessions

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Set B = {x, x, y, 9, 10, 16, 16}

Set B has 7 members and x and y are distinct positive integers. If x is the mode of Set B and the mean of Set B is 12, which of the following is a valid value of x that would cause the standard deviation of the set to be greatest?

Re: Set B has 7 members and x and y are distinct positive integers. If x
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29 Mar 2017, 10:54

Bunuel wrote:

Set B = {x, x, y, 9, 10, 16, 16}

Set B has 7 members and x and y are distinct positive integers. If x is the mode of Set B and the mean of Set B is 12, which of the following is a valid value of x that would cause the standard deviation of the set to be greatest?

A. 9 B. 10 C. 12 D. 16 E. 18

clearly its D

if x=18 then y =negative value ,which is not possible as y is positive thus if x =16 the mode is 16 and then there will be 4 extreme points from mean 12,making set more disperse

Set B has 7 members and x and y are distinct positive integers. If x
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30 Mar 2017, 00:27

2

Bunuel wrote:

Set B = {x, x, y, 9, 10, 16, 16}

Set B has 7 members and x and y are distinct positive integers. If x is the mode of Set B and the mean of Set B is 12, which of the following is a valid value of x that would cause the standard deviation of the set to be greatest?

A. 9 B. 10 C. 12 D. 16 E. 18

Mode = x but since 16 has already appeared twice so x must be equal to an existing term of the set other than 16 or 16 itself Mean = 12 => 2x+y+51 = 12*7 => 2x+y = 84-51 = 33

CONCEPT: STANDARD DEVIATION is MAXIMUM when new term is FARTHEST from mean

so the value of x farthest from mean which can set mode 16 must be 16 itself

Answer: Option D
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Re: Set B has 7 members and x and y are distinct positive integers. If x
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19 Apr 2017, 20:45

Bunuel wrote:

Set B = {x, x, y, 9, 10, 16, 16}

Set B has 7 members and x and y are distinct positive integers. If x is the mode of Set B and the mean of Set B is 12, which of the following is a valid value of x that would cause the standard deviation of the set to be greatest?

A. 9 B. 10 C. 12 D. 16 E. 18

From the given information we can deduce that 2x+ y = 33

If the value of x is 16, y=1 (the least positive integer), gives us maximum range = 15.

Re: Set B has 7 members and x and y are distinct positive integers. If x
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14 Jan 2019, 10:03

Top Contributor

Bunuel wrote:

Set B = {x, x, y, 9, 10, 16, 16}

Set B has 7 members and x and y are distinct positive integers. If x is the mode of Set B and the mean of Set B is 12, which of the following is a valid value of x that would cause the standard deviation of the set to be greatest?

A. 9 B. 10 C. 12 D. 16 E. 18

The mean of Set B is 12 We can write: (x + x + y + 9 + 10 + 16 + 16)/7 = 12 So: x + x + y + 9 + 10 + 16 + 16 = 84 Simplify: 2x + y + 51 = 84 So, 2x + y = 33

x is the mode of Set B If x = 9, 10, or 16, the mode of Set B will equal x So, x can have 3 possible values.

Let's test all 3 cases: case i: x = 9 If 2x + y = 33, and x = 9, then y = 15 So, our two values are: x = 9 & y = 15

case ii: x = 10 If 2x + y = 33, and x = 10, then y = 13 So, our two values are: x = 10 & y = 13

case iii: x = 16 If 2x + y = 33, and x = 16, then y = 1 So, our two values are: x = 16 & y = 1

Which of the following is a valid value of x that would cause the standard deviation of the set to be greatest? To maximize the Standard Deviation, we must find the pair of values that are farthest from the mean (mean = 12) The pair of values x = 16 and y = 1 are the farthest from the mean.

So, x = 16 will maximize the Standard Deviation Answer: D

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Re: Set B has 7 members and x and y are distinct positive integers. If x &nbs
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14 Jan 2019, 10:03