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21 Nov 2022, 09:30
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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:
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Question Stats:
82% (00:57) correct
18%
(01:06)
wrong
based on 33
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The standard deviation of the five values 2, 4, 6, 8, 10 is σ. For which of the following lists is the standard deviation of the values in the list equal to σ?
I. 1, 3, 5, 7, 9
II. 3, 5, 7, 9, 11
III. 4, 8, 12, 16, 20
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
I. 1, 3, 5, 7, 9
II. 3, 5, 7, 9, 11
III. 4, 8, 12, 16, 20
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
Updated on: 21 Nov 2022, 20:37
Originally posted by BrushMyQuant on 21 Nov 2022, 09:56.
Last edited by BrushMyQuant on 21 Nov 2022, 20:37, edited 3 times in total.
Last edited by BrushMyQuant on 21 Nov 2022, 20:37, edited 3 times in total.
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Given that Standard Deviation(SD) of the set 2, 4, 6, 8, 10 is σ and we need to find for which of the following lists is the standard deviation of the values in the list equal to σ?
I. 1, 3, 5, 7, 9
II. 3, 5, 7, 9, 11
III. 4, 8, 12, 16, 20
Theory
I. 1, 3, 5, 7, 9
We can get this set by subtracting 1 from all the terms in the set 2, 4, 6, 8, 10 by 1
=> SD of 1, 3, 5, 7, 9 = SD of 2, 4, 6, 8, 10 = σ => TRUE
II. 3, 5, 7, 9, 11
We can get this set by adding 1 to all the terms in the set 2, 4, 6, 8, 10 by 1
=> SD of 3, 5, 7, 9, 11 = SD of 2, 4, 6, 8, 10 = σ => TRUE
III. 4, 8, 12, 16, 20
We can get this set by multiplying all the terms in the set 2, 4, 6, 8, 10 by 2
=> SD of 4, 8, 12, 16, 20 = 2 * SD of 2, 4, 6, 8, 10 = 2σ => FALSE
So, Answer will be D.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Attaching a brief of various properties
Relationships.png [ 94.25 KiB | Viewed 2252 times ]
I. 1, 3, 5, 7, 9
II. 3, 5, 7, 9, 11
III. 4, 8, 12, 16, 20
Theory
- → SD is an indication of how spread the terms are as compared to the mean.
→ If same number is added/subtracted from all the numbers in a set then the SD does not change
→ If all the numbers in the set are multiplied/divided by the same number(k) then the Standard Deviation also gets multiplied/divided by the modulus of that number |k|.
I. 1, 3, 5, 7, 9
We can get this set by subtracting 1 from all the terms in the set 2, 4, 6, 8, 10 by 1
=> SD of 1, 3, 5, 7, 9 = SD of 2, 4, 6, 8, 10 = σ => TRUE
II. 3, 5, 7, 9, 11
We can get this set by adding 1 to all the terms in the set 2, 4, 6, 8, 10 by 1
=> SD of 3, 5, 7, 9, 11 = SD of 2, 4, 6, 8, 10 = σ => TRUE
III. 4, 8, 12, 16, 20
We can get this set by multiplying all the terms in the set 2, 4, 6, 8, 10 by 2
=> SD of 4, 8, 12, 16, 20 = 2 * SD of 2, 4, 6, 8, 10 = 2σ => FALSE
So, Answer will be D.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Attaching a brief of various properties
Attachment:
Relationships.png [ 94.25 KiB | Viewed 2252 times ]
21 Nov 2022, 12:04
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BrushMyQuant
Hi BrushMyQuant
I am under the impression that the SD changes by the same factor on multiplication and not the square root of the factor (as indicated in the highlighted portion).
Can you please confirm this ?
If I understand the context correct, the statement caters to below scenarios -
Example 1
Set A = {10, 12, 23, 23, 16, 23, 21, 16}
\(SD_A\) = 4.8989794855664
Each term in set A is multiplied by 2 to form set B
Set B = {20, 24, 46, 46, 32, 46, 42, 32}
\(SD_B\) = 9.7979589711327
\(SD_B\) = 2 * \(SD_A\)
Example 2
Set A = {2, 4, 6, 8, 10}
\(SD_A\) = 2.8284271247462
Each number in set A is divided by 2 to form set B.
Set B = {1, 2, 3, 4, 5}
\(SD_B\) = 1.4142135623731
\(SD_B\) = \(\frac{1}{2}\) * \(SD_A\)
IMO the statement should be -
If all numbers in the set are multiplied/divided by the same number then the SD gets multiplied/divided by the modulus of that number
Please let me know if I am missing anything.
