If the average of ten numbers is 10, then which of the following could be the standard deviation of the ten numbers?

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If the average of ten numbers is 10, then which of the following could be the standard deviation of the ten numbers?

I. 0
II. 10
III. 20

A. I only
B. I and II
C. I and III
D. II and III
E. I, II, and III



OA E

Source: Princeton Review

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BTGmoderatorDC wrote:
Sun Dec 05, 2021 7:23 pm
If the average of ten numbers is 10, then which of the following could be the standard deviation of the ten numbers?

I. 0
II. 10
III. 20

A. I only
B. I and II
C. I and III
D. II and III
E. I, II, and III



OA E

Source: Princeton Review
First recognize that, if all 10 numbers are 10 to get the set {10, 10, 10, 10, 10, 10, 10, 10, 10, 10}, then the standard deviation of the set is 0.

Now let's take one of the numbers in the set and change it to 11 to get {10, 10, 10, 10, 10, 10, 10, 10, 10, 11}.
In this case, the standard deviation is greater than 0

If we change that number to 12 to get {10, 10, 10, 10, 10, 10, 10, 10, 10, 12}, then the standard deviation of the set is even bigger.
In fact, by increasing the value of that last number, we kind of make the standard deviation as big as we want.

In other words, the set of values can have ANY standard deviation from 0 to any positive number.

Answer: E
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