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# In the list of different positive numbers above, the arithmetic mean

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In the list of different positive numbers above, the arithmetic mean  [#permalink]

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06 Jun 2017, 08:53
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Difficulty:

65% (hard)

Question Stats:

53% (01:29) correct 47% (01:11) wrong based on 194 sessions

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a, b, c, d, e

In the list of different positive numbers above, the arithmetic mean is c. Which of the following changes to the list would necessarily increase the standard deviation?

A. Increase the value of b by 20%
B. Add the values (c + 3) and (c – 3) to the list
C. Add 10 to each value in the list
D. Multiply each value by -5
E. Divide each value by 2

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Re: In the list of different positive numbers above, the arithmetic mean  [#permalink]

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07 Jun 2017, 10:27
2
2
Bunuel wrote:
a, b, c, d, e

In the list of different positive numbers above, the arithmetic mean is c. Which of the following changes to the list would necessarily increase the standard deviation?

A. Increase the value of b by 20%
B. Add the values (c + 3) and (c – 3) to the list
C. Add 10 to each value in the list
D. Multiply each value by -5
E. Divide each value by 2

Standard deviation INCREASES when the gap among values of the set increase.

A) Increase in value of b may not necessarily increase rather it may decrease the standard deviation if increased value of b becomes closer to mean
B) Adding these two values in list may decrease the standard deviation if it was already greater than 3
C) addition or subtraction of a constant in each element doesn't change the standard deviation as the deviation among terms remain constant
D) the gap among terms will also get multiplied by -5 and hence since deviation. Becomes 5 times so the standard deviation will definitely increase.

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##### General Discussion
Director
Joined: 21 Mar 2016
Posts: 522
Re: In the list of different positive numbers above, the arithmetic mean  [#permalink]

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07 Jun 2017, 10:18
luks like A...

B-- the two value c+3 and c-3 will shrink the SD because both add up the same value to average as c
C-- no change in SD
D-- SD goes down by 5%
E-- SD gets divided by 2..

must be A
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Re: In the list of different positive numbers above, the arithmetic mean  [#permalink]

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09 Sep 2018, 05:47
GMATinsight wrote:
Bunuel wrote:
a, b, c, d, e

In the list of different positive numbers above, the arithmetic mean is c. Which of the following changes to the list would necessarily increase the standard deviation?

A. Increase the value of b by 20%
B. Add the values (c + 3) and (c – 3) to the list
C. Add 10 to each value in the list
D. Multiply each value by -5
E. Divide each value by 2

Standard deviation INCREASES when the gap among values of the set increase.

A) Increase in value of b may not necessarily increase rather it may decrease the standard deviation if increased value of b becomes closer to mean
B) Adding these two values in list may decrease the standard deviation if it was already greater than 3
C) addition or subtraction of a constant in each element doesn't change the standard deviation as the deviation among terms remain constant
D) the gap among terms will also get multiplied by -5 and hence since deviation. Becomes 5 times so the standard deviation will definitely increase.

Hello GMATinsight, nice explanation could you please provide examples for all options if you dont mind ?
Manager
Joined: 24 Sep 2018
Posts: 139
Re: In the list of different positive numbers above, the arithmetic mean  [#permalink]

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25 Sep 2018, 22:22
2
This problem showcases a few important properties related to standard deviation. Since standard deviation deals heavily with the average distance between the data points and the mean, several rules apply for how changing all terms in a set will affect the standard deviation:
Quote:
If all terms are multiplied by a constant with an absolute value greater than 1, the standard deviation will increase. Consider the set 1, 2, 3, 4, 5. If all terms were multiplied by -5 (as correct answer choice D suggests), the terms would then be -5, -10, -15, -20, and -25. Notice that they are now much more spread out around the new mean (distances of 10, 5, 0, 5, and 10 as opposed to previously, 2, 1, 0, 1, and 2). Multiplying by an absolute value greater than 1 spreads the data points out farther, increasing the standard deviation
Quote:
If all the terms are divided by a constant with an absolute value greater than 1, the standard deviation will decrease. Consider that same sample set of 1, 2, 3, 4, 5. If you divide each term by 2 as answer choice E suggests, you'll end up with 0.5, 1, 1.5, 2, and 2.5. The values are closer together, showing that the standard deviation has decreased.
Quote:
if you add or subtract a constant to each term (as choice C suggests), the standard deviation will not change. You've simply shifted the set, but you haven't changed the distance between each value and the mean. Consider performing the suggested operation from choice C to the sample list. 1, 2, 3, 4, 5 becomes 11, 12, 13, 14, 15. The new mean is 13, but the distances stay the same (2, 1, 0, 1, 2).
Quote:
Among the other choices, choice A is incorrect because you do not know where on the number line b is in relation to the mean. If increasing it by 20% gets it closer to the mean, the variance would decrease; if it moves it farther, the variance would increase.
Quote:
And choice B is incorrect because you don't know how the other terms relate to c. If they're spread very far apart (1000, 2000, 3000, 4000, 5000, for example) then adding two new values only three apart from the mean will substantially decrease the standard deviation. But if they're already very close to the mean (1.1, 1.2, 1.3, 1.4, 1.5) then the two new terms (-2.3 and 4.3) would be the outliers, spreading the data farther apart.

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In the list of different positive numbers above, the arithmetic mean  [#permalink]

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25 Sep 2018, 22:33
1
dave13 wrote:
GMATinsight wrote:
Bunuel wrote:
a, b, c, d, e

In the list of different positive numbers above, the arithmetic mean is c. Which of the following changes to the list would necessarily increase the standard deviation?

A. Increase the value of b by 20%
B. Add the values (c + 3) and (c – 3) to the list
C. Add 10 to each value in the list
D. Multiply each value by -5
E. Divide each value by 2

Standard deviation INCREASES when the gap among values of the set increase.

A) Increase in value of b may not necessarily increase rather it may decrease the standard deviation if increased value of b becomes closer to mean
B) Adding these two values in list may decrease the standard deviation if it was already greater than 3
C) addition or subtraction of a constant in each element doesn't change the standard deviation as the deviation among terms remain constant
D) the gap among terms will also get multiplied by -5 and hence since deviation. Becomes 5 times so the standard deviation will definitely increase.

Hello GMATinsight, nice explanation could you please provide examples for all options if you dont mind ?

dave13 There you go

Standard deviation INCREASES when the gap among values of the set increase.

A) Increase in value of b may not necessarily increase rather it may decrease the standard deviation if increased value of b becomes closer to mean
In Set {1, 2, 3, 4, 5} if b i.e. 2 is increased by 20% the new set becomes {1, 2.4, 3, 4, 5} and the standard deviation of the new set is less than standard deviation of previous set

B) Adding these two values in list may decrease the standard deviation if it was already greater than 3
In Set {100, 200, 300, 400, 500} if (c-3) and (c+3) are included then the new set becomes {100, 200, 297, 300, 303, 400, 500} and the standard deviation of the new set is less than standard deviation of previous set

C) addition or subtraction of a constant in each element doesn't change the standard deviation as the deviation among terms remain constant
In Set {1, 2, 3, 4, 5} if a constant 2 is added in each term of the set then the new set becomes {3, 4, 5, 6, 7} and the standard deviation of the new set is is same as the standard deviation of previous set

D) the gap among terms will also get multiplied by -5 and hence since deviation. Becomes 5 times so the standard deviation will definitely increase.
In Set {1, 2, 3, 4, 5} if -5 is multiplied in each term of the set then the new set becomes {-5, -10, -15, -20, -25} and the standard deviation of the new set is GREATER than standard deviation of previous set as the gap between successive terms is becomes five times greater which is determinant of the standard deviation

I hope this helps!!!
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In the list of different positive numbers above, the arithmetic mean   [#permalink] 25 Sep 2018, 22:33
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