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07 Nov 2022, 10:50
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
23% (01:54) correct
77%
(01:24)
wrong
based on 53
sessions
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The average of a list of 17 numbers is 0, and the standard deviation of these numbers is 40. If a new number is added to the list, the average remains the same, then what is the new standard deviation of the list approximately?
A. 36.80
B. 38.87
C. 39.88
D. 40
E. 41
A. 36.80
B. 38.87
C. 39.88
D. 40
E. 41
08 Nov 2022, 13:35
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Afroditee
This question seems far-fetched from what GMAT usually tests for Standard Deviation.
The standard deviation of a set decreases when a number equal to the mean is added to the set. Hence we can eliminate D and E.
Among A, B and C , to get the value of the new SD, we need to do a bit of calculation.
SD = \(\sqrt{\frac{D}{n}}\)
D is the sum of square of the distance of each term from the mean.
40 = \(\sqrt{\frac{D}{17}}\)
D = \(40^2\) * 17
With the addition of new term, which is equal to the mean, D will not change
New SD = \(\sqrt{\frac{40^2 * 17 }{ 18 }}\)
= 40 * \(\frac{4.125 }{ 4.25 }\)
= 4 * \(\frac{165}{17}\)
= \(\frac{660}{17}\)
= 38.8
Option B
