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26 Jul 2022, 11:30
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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:
5%
(low)
Question Stats:
91% (00:40) correct
9%
(01:12)
wrong
based on 53
sessions
History
Date
Time
Result
Not Attempted Yet
(I) {55, 56, 57, 58, 59}
(II) {41, 57, 57, 57, 73}
(III) {57, 57, 57, 57, 57}
Which of the following lists Sets I, II, and III in order from least standard deviation to greatest standard deviation?
(A) I, II, III
(B) I, III, II
(C) II, III, I
(D) III, I, II
(E) III, II, I
(II) {41, 57, 57, 57, 73}
(III) {57, 57, 57, 57, 57}
Which of the following lists Sets I, II, and III in order from least standard deviation to greatest standard deviation?
(A) I, II, III
(B) I, III, II
(C) II, III, I
(D) III, I, II
(E) III, II, I
31 Jul 2022, 22:10
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Theory
If we look at the sets then at first glance following is the observation
(I) {55, 56, 57, 58, 59} -> Numbers are very close to the Mean (which is 57). So, SD will be Small.
(II) {41, 57, 57, 57, 73} -> Two numbers are very far from the mean of 57. Both 41 and 73 are at a distance of 16 from 57.(on either side)
(III) {57, 57, 57, 57, 57} -> All numbers are same so SD will be 0.
So, Sequence of SD will be
III < I < II
So, Answer will be D.
If you want to learn how to calculate SD then the calculation is as follows
(I) {55, 56, 57, 58, 59}
Mean = 57 (middle value as the numbers are consecutive numbers)
Variance = \(\frac{(55-57)^2 + (56-57)^2 + (57-57)^2 + (58-57)^2 + (59-57)^2 }{ 5}\)
= \(\frac{(-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 }{ 5}\)
= \(\frac{4 + 1 + 0 + 1 + 4 }{ 5}\) = \(\frac{10}{2}\) = 5
SD = \(\sqrt{Variance}\) = \(\sqrt{5}\)
(II) {41, 57, 57, 57, 73}
Mean = 57 (middle value as the numbers are consecutive numbers)
Variance = \(\frac{(41-57)^2 + (57-57)^2 + (57-57)^2 + (57-57)^2 + (73-57)^2 }{ 5}\)
= \(\frac{(-16)^2 + 0^2 + 0^2 + 0^2 + 16^2 }{ 5}\)
= \(\frac{256 + 0 + 0 + 0 + 256 }{ 5}\) = \(\frac{512}{2}\) = 102.4
SD = \(\sqrt{Variance}\) = \(\sqrt{102.4}\) ~ 10
(II) {57, 57, 57, 57, 57}
Mean = 57 (middle value as the numbers are consecutive numbers)
Variance = \(\frac{(57-57)^2 + (57-57)^2 + (57-57)^2 + (57-57)^2 + (57-57)^2 }{ 5}\)
= \(\frac{0^2 + 0^2 + 0^2 + 0^2 + 0^2 }{ 5}\)
= \(\frac{0 + 0 + 0 + 0 + 0 }{ 5}\) = 0
SD = \(\sqrt{Variance}\) = \(\sqrt{0}\) = 0
So, Sequence of SD will be
III < I < II
So, Answer will be D.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
- ➡ Standard Deviation (SD) is an indication of how spread the values are as compared to the Mean
➡ SD is equal to the Root Mean Square(RMS) of the distance of the values from the Mean
If we look at the sets then at first glance following is the observation
(I) {55, 56, 57, 58, 59} -> Numbers are very close to the Mean (which is 57). So, SD will be Small.
(II) {41, 57, 57, 57, 73} -> Two numbers are very far from the mean of 57. Both 41 and 73 are at a distance of 16 from 57.(on either side)
(III) {57, 57, 57, 57, 57} -> All numbers are same so SD will be 0.
So, Sequence of SD will be
III < I < II
So, Answer will be D.
If you want to learn how to calculate SD then the calculation is as follows
(I) {55, 56, 57, 58, 59}
Mean = 57 (middle value as the numbers are consecutive numbers)
Variance = \(\frac{(55-57)^2 + (56-57)^2 + (57-57)^2 + (58-57)^2 + (59-57)^2 }{ 5}\)
= \(\frac{(-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 }{ 5}\)
= \(\frac{4 + 1 + 0 + 1 + 4 }{ 5}\) = \(\frac{10}{2}\) = 5
SD = \(\sqrt{Variance}\) = \(\sqrt{5}\)
(II) {41, 57, 57, 57, 73}
Mean = 57 (middle value as the numbers are consecutive numbers)
Variance = \(\frac{(41-57)^2 + (57-57)^2 + (57-57)^2 + (57-57)^2 + (73-57)^2 }{ 5}\)
= \(\frac{(-16)^2 + 0^2 + 0^2 + 0^2 + 16^2 }{ 5}\)
= \(\frac{256 + 0 + 0 + 0 + 256 }{ 5}\) = \(\frac{512}{2}\) = 102.4
SD = \(\sqrt{Variance}\) = \(\sqrt{102.4}\) ~ 10
(II) {57, 57, 57, 57, 57}
Mean = 57 (middle value as the numbers are consecutive numbers)
Variance = \(\frac{(57-57)^2 + (57-57)^2 + (57-57)^2 + (57-57)^2 + (57-57)^2 }{ 5}\)
= \(\frac{0^2 + 0^2 + 0^2 + 0^2 + 0^2 }{ 5}\)
= \(\frac{0 + 0 + 0 + 0 + 0 }{ 5}\) = 0
SD = \(\sqrt{Variance}\) = \(\sqrt{0}\) = 0
So, Sequence of SD will be
III < I < II
So, Answer will be D.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
07 Feb 2026, 08:08
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