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Tha standard deviation
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25 Oct 2021, 05:34
25 Oct 2021, 05:34
Expert Reply
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Quantity A |
Quantity B |
The standard deviation of 4,6,8,10,12 |
The standard deviation of 8,8,8,8,8 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
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Re: Tha standard deviation
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25 Oct 2021, 08:05
25 Oct 2021, 08:05
1
Carcass wrote:
Quantity A |
Quantity B |
The standard deviation of 4,6,8,10,12 |
The standard deviation of 8,8,8,8,8 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Key property #1: The standard deviation of a set of numbers is always greater than or equal to 0
Key property #2: If the numbers in a set are all identical, and the standard deviation of that set is zero
By property #2, the standard deviation of {8,8,8,8,8} is 0
By properties #1 and #2, the standard deviation of {4,6,8,10,12} is not 0, which means the standard deviation must be positive.
So, we have:
QUANTITY A: Some positive value
QUANTITY B: 0
Answer: A
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General Discussion
Re: Tha standard deviation
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07 Nov 2024, 13:57
07 Nov 2024, 13:57
1
Because of which standard deviation cannot be less than zero, and the series all consisting of same numbers have 0 standard deviation, the answer A does make sense. Same numbers have zero standard deviation. Any series that has at least one different number will have a standard deviation greater than zero.
