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# Which of the following sets has the greatest standard deviation?

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Math Expert
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Which of the following sets has the greatest standard deviation?  [#permalink]

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19 Dec 2016, 08:43
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87% (01:02) correct 13% (01:10) wrong based on 86 sessions

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Which of the following sets has the greatest standard deviation?

A. {1, 4, 12, 16, 17}
B. {3, 4, 7, 18, 18}
C. {2, 5, 13, 17, 23}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}

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Re: Which of the following sets has the greatest standard deviation?  [#permalink]

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19 Dec 2016, 09:54
By calculating mean of each Set and then checking which no. Is farther from mean we just left with option D

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Which of the following sets has the greatest standard deviation?  [#permalink]

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19 Dec 2016, 09:59
Standard deviation is a square root of the sum of squired differences between elements of the set and set’s mean divided by the # of elements. Wordy, but the logic is that the greater the difference of the elements from the mean the greater the deviation. If set contains some “peaks” which are far from the mean, this distance will be squared in calculation of the variation.

All the given sets have similar means, its value will be somewhere between 8 and 12. But set D has negative element -50, which when deducted from he mean and then squared will add rather big value to our variation $$(60 + something)^2$$.

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Re: Which of the following sets has the greatest standard deviation?  [#permalink]

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03 Jan 2017, 16:47
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Bunuel wrote:
Which of the following sets has the greatest standard deviation?

A. {1, 4, 12, 16, 17}
B. {3, 4, 7, 18, 18}
C. {2, 5, 13, 17, 23}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}

The standard deviation is a sophisticated measure that relies in part on the distance of each data value from the mean. In general, the farther the data values are from the mean, the larger the standard deviation. So, let’s find the mean of each data set first.

A. (1 + 4 + 12 + 16 + 17)/5 = 50/5 = 10
B. (3 + 4 + 7 +18 +18)/5 = 50/5 = 10
C. (2 + 5 + 13 + 17 + 23)/5 = 50/5 =10
D. (-50 + 2 + 33 + 34 + 35)/5 = 50/5 = 10
E. (0 + 0 + 0 + 19+ 31)/5 = 50/5 = 10

As we can see, all the data sets have a mean of 10. Now, for each data set, we need to find how far away each value is from the mean. Let’s look at the data sets again.

A. {1, 4, 12, 16, 17}
B. {3, 4, 7, 18, 18}
C. {2, 5, 13, 17, 23}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}

As we can see, the data values from set D are the farthest from its mean out of all the data sets (four of its 5 values, -50, 33, 34, and 35, are farther from 10 than any values in the other data sets); thus, set D has the greatest standard deviation.

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Which of the following sets has the greatest standard deviation?  [#permalink]

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24 Jun 2018, 23:58
JeffTargetTestPrep wrote:
Bunuel wrote:
Which of the following sets has the greatest standard deviation?

A. {1, 4, 12, 16, 17}
B. {3, 4, 7, 18, 18}
C. {2, 5, 13, 17, 23}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}

The standard deviation is a sophisticated measure that relies in part on the distance of each data value from the mean. In general, the farther the data values are from the mean, the larger the standard deviation. So, let’s find the mean of each data set first.

A. (1 + 4 + 12 + 16 + 17)/5 = 50/5 = 10
B. (3 + 4 + 7 +18 +18)/5 = 50/5 = 10
C. (2 + 5 + 13 + 17 + 23)/5 = 50/5 =10
D. (-50 + 2 + 33 + 34 + 35)/5 = 50/5 = 10
E. (0 + 0 + 0 + 19+ 31)/5 = 50/5 = 10

As we can see, all the data sets have a mean of 10. Now, for each data set, we need to find how far away each value is from the mean. Let’s look at the data sets again.

A. {1, 4, 12, 16, 17}
B. {3, 4, 7, 18, 18}
C. {2, 5, 13, 17, 23}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}

As we can see, the data values from set D are the farthest from its mean out of all the data sets (four of its 5 values, -50, 33, 34, and 35, are farther from 10 than any values in the other data sets); thus, set D has the greatest standard deviation.

Jeff, for options C and D, I am getting a total of 60 and 54, resulting in a mean of 12 and 10.8 respectively.
But even then, option D has the highest deviation. Am I doing something wrong?
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Re: Which of the following sets has the greatest standard deviation?  [#permalink]

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25 Jun 2018, 03:21
Is it necessary to calculate mean?
At a glance it was obvious that Set D had the most scattered vaues
Re: Which of the following sets has the greatest standard deviation? &nbs [#permalink] 25 Jun 2018, 03:21
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