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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:
35%
(medium)
Question Stats:
66% (01:09) correct
34%
(01:15)
wrong
based on 143
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History
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Time
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Not Attempted Yet
Which of the following set has the smallest standard deviation ?
A. {2, 2, 3, 5, 7}
B. {2, 2, 2, 2, 79}
C. {2, 2, 3, 4, 7}
D. {2, 2, 6.9, 4, 3}
E. {8, 2, 2, 3, 5}
A. {2, 2, 3, 5, 7}
B. {2, 2, 2, 2, 79}
C. {2, 2, 3, 4, 7}
D. {2, 2, 6.9, 4, 3}
E. {8, 2, 2, 3, 5}
31 Jan 2020, 22:44
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Bunuel
Solution:
We will solve this problem by using the definition of standard deviation.
The best method to solve this problem is to calculate the mean of each set and after that, we will find the difference between mean and entry of the set. The least scattered set will have the least standard deviation.
Option A: \(\{2, 2, 3, 5, 7\}\)
- • Mean = \(\frac{19}{5} =3.8\)
• Now, The difference between mean and each element =\(\{-1.8, -1.8, -0.8, 1.2, 3.2\}\)
- • Mean = \(\frac{87}{5}=17.4\)
• Now,The difference between mean and each element =\( \{-15.4, -15.4, -15.4, 15.4, 61.6\}\)
- • Mean = \(18/5= 3.6\)
• Now,The difference between mean and each element =\( \{-1.6, -1.6, -0.6, 0.4, 3.4\}\)
- • Mean =\(\frac{ 17.9}{5} = 3.58\)
• Now,The difference between mean and each element =\( \{-1.58, -1.58, 3.32, 0.42, -0.58\}\)
- • Mean = \(\frac{20}{5}=4\)
• Now,The difference between mean and each element = \(\{4, -2, -2, -1, 1\}\)
hence, the correct answer is Option D.
