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24 Sep 2021, 05:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (01:41) correct
44%
(01:35)
wrong
based on 160
sessions
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Set A: \(a, \ b, \ c, \ d, \ e\)
Set B: \(\frac{2}{3}a - 6, \ \frac{2}{3}b - 6, \ \frac{2}{3}c - 6, \ \frac{2}{3}d - 6, \ \frac{2}{3}e - 6\)
If the standard deviation of Set B is 12.5, then what is the standard deviation of Set A?
A. 12.5
B. 18.25
C. 18.5
D. 18.75
E. 19
Set B: \(\frac{2}{3}a - 6, \ \frac{2}{3}b - 6, \ \frac{2}{3}c - 6, \ \frac{2}{3}d - 6, \ \frac{2}{3}e - 6\)
If the standard deviation of Set B is 12.5, then what is the standard deviation of Set A?
A. 12.5
B. 18.25
C. 18.5
D. 18.75
E. 19
24 Sep 2021, 06:36
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If you add the same value to everything in a set, you don't change any of the distances within the set, so you don't change the standard deviation. So if 12.5 is the standard deviation of set B, then 12.5 is also the standard deviation of the set
2a/3, 2b/3, 2c/3, 2d/3, 2e/3
If you multiply every value in a set by a constant positive number, you correspondingly stretch out the distances in the set (or shrink them, if you multiply by something less than 1). So the standard deviation is also multiplied by that constant. So if we multiply every value in the set above by 3/2, to get set A, we'll be multiplying our standard deviation by 3/2, and the answer is (3/2)(12.5) = (3/2)(25/2) = 75/4 = 18.75.
2a/3, 2b/3, 2c/3, 2d/3, 2e/3
If you multiply every value in a set by a constant positive number, you correspondingly stretch out the distances in the set (or shrink them, if you multiply by something less than 1). So the standard deviation is also multiplied by that constant. So if we multiply every value in the set above by 3/2, to get set A, we'll be multiplying our standard deviation by 3/2, and the answer is (3/2)(12.5) = (3/2)(25/2) = 75/4 = 18.75.
24 Sep 2021, 11:26
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IanStewart
had a doubt why dint the -6 in each of the terms in set b not be considered
