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What can be said about a set of data with a standard deviation of​ 0? ​(This is a reading assessment question. Be certain of your answer because you only get one attempt on this​ question.) Choose the correct answer below. A. All the observations are the same value. B. All the observations are 0. C. For every positive​ value, there is a corresponding negative value​ (as in 4 and −​4; 6 and −​6).

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Answer:

A.) All the observations are the same value

Step-by-step explanation:

One of the statistical measures used to determine the spread or variability of a dataset is the variance or standard deviation. The standard deviation determines how a set of value varies about the mean value.

Mathematically,

Variability or spread = mean + number of standard deviations

Hence, a standard deviation of 0 ; means they there is no variability in the dataset. Hence, a standard deviation of 0 means all observations are of the same value.

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For a set of data with a standard deviation of 0, the correct option is:

A: "All the observations are the same value."

What is the standard deviation?

For a given set {x₁, x₂, ...} with N elements.

With a mean M, we define the standard deviation as:

[tex]S= \sqrt{\frac{\sum (x_i - M)^2}{N - 1} }[/tex]

Notice that, because we have a squared element in the sum, all the elements of the sum are positive. So if we have a single value of the set that is different than the mean, then the standard deviation will be larger than zero.

Then the only case where the standard deviation is zero is the case where all the elements of the set are equal to the mean of the set, and that only happens if all the elements of the set are equal.

So the correct option is A:

"All the observations are the same value. "

If you want to learn more about standard deviation, you can read:

https://brainly.com/question/15858152

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