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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
48% (01:55) correct
52%
(01:25)
wrong
based on 396
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Which of the following sets has the smallest standard deviation?
A. {2, 5, 13, 17, 23}
B. {3, 4, 7, 18, 18}
C. {1, 4, 12, 16, 17}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}
A. {2, 5, 13, 17, 23}
B. {3, 4, 7, 18, 18}
C. {1, 4, 12, 16, 17}
D. {-50, 2, 33, 34, 35}
E. {0, 0, 0, 19, 31}
07 Sep 2017, 03:19
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TheMastermind
Hi TheMastermind ,
Thanks for tagging me in this. I love this type of questions.
Here, you need to know one important concept.
Standard deviation is the amount of data that is farthest from the average of the numbers.
So, all you need to do is find out the average of each set and then determine the sum of the gaps of each numbers from the mean.
The lower the gap, the smaller the Standard Deviation.
Let me solve first 3 options for you. Rest I believe you can solve ( I didn't because I could see there will be big gaps.)
A. {2, 5, 13, 17, 23}
Mean = 12.
Difference of each term from this mean = 10, 7, 1,5,11.
Sum of these gaps/differences = 34.
B. {3, 4, 7, 18, 18}
Mean = 10.
Difference of each term from this mean = 7,6,3,8,8.
Sum of these gaps/differences = 32.
C. {1, 4, 12, 16, 17}
Mean = 10.
Difference of each term from this mean = 9, 6, 2, 6, 7.
Sum of these gaps/differences = 30.
Since C has the lowest GAP. C will have the lowest Standard Deviation. Hence, the answer.
Does that make sense?
General Discussion
Bunuel
Ans C
A,D &E are out since their ranges are high in respect of other (option B & C) sets.
it also means that the deviation from mean is high compared to other sets
B out ,as it has 2 extreme points from mean(ie 10)
Ans C
