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What is the standard deviation of the values

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What is the standard deviation of the values

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What is the standard deviation of the values of the 20 coins in a certain jar ?

1. The average (arithmetic mean ) value of the coins in the jar is 25 cents .

2. All 20 coins in the jar have the same value .

How will i find the best statement?

OA B

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lheiannie07 wrote:
What is the standard deviation of the values of the 20 coins in a certain jar ?

1. The average (arithmetic mean ) value of the coins in the jar is 25 cents.

2. All 20 coins in the jar have the same value.

How will i find the best statement?

OA B
Standard deviation (SD) is a measure of the spread or how far the values are w.r.t the mean. Closer the values are to the mean, less is the SD, and vice-versa.

1. The average (arithmetic mean ) value of the coins in the jar is 25 cents.

We do not know how many coins of different denominations are there in the jar. If all the coins are of 25 cents, SD = 0; however, even if two coins are not 25 cents, SD > 0. Insufficient.

2. All 20 coins in the jar have the same value.

Since all the 20 coins in the jar have the same value, their mean = value of each of the coin. Thus, there is no deviation at all. SD = 0. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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lheiannie07 wrote:
What is the standard deviation of the values of the 20 coins in a certain jar ?

1. The average (arithmetic mean ) value of the coins in the jar is 25 cents .

2. All 20 coins in the jar have the same value .
Target question: What is the standard deviation of the values of the 20 coins in a certain jar ?

Statement 1: The average (arithmetic mean ) value of the coins in the jar is 25 cents .
There are several cases that satisfy statement 1. Here are two:
Case a: All 20 coins are quarters (each is worth $0.25). This meets this condition that the average value is 25 cents. In this case, the standard deviation EQUALS 0
Case b: All 20 coins are NOT quarters. In this case, the standard deviation does NOT equal 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: All 20 coins in the jar have the same value
The means the standard deviation EQUALS 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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Standard deviation of a set of numbers is a non-negative quantity which equals (maximum number - minimum number) in the set.
Statement 1: We are given the mean of the set of numbers. We can’t find the maximum and the minimum number from this information .Hence, Insufficient.
Statement 2: It is given that all 20 coins in the jar have the same value. This means the S.D = 0.
Hence, Sufficient.

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Standard deviation of a set of numbers is a non-negative quantity which equals zero, if and only if all the values in the set are numerically equal.
Statement 1: We are given the mean of the set of numbers. We can’t find the standard deviation from this information alone. Hence, Insufficient.
Statement 2: It is given that all 20 coins in the jar have the same value. This definitely implies thatstandard deviation equals zero. Hence, Sufficient.

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