Question

A set of data has ten numbers.The mean of the data is 12 and the standard deviation is 0. What values could make up a data set with these statistics?

Answer 1

Answer:

6,4,2,10,18,15,35,10,15,5

Answer 2

We know that for a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

$M = \frac{x_1 + x_2 + ... + x_n}{N}$

And the standard deviation is given by:

$S = \sqrt{\frac{\sum (x_i - M)^2}{N - 1} }$

With this, we will find that our set is: {12, 12, 12, 12, 12, 12, 12, 12, 12, 12}

To get this we need to see the information given:

The set has 10 elements.

The mean of the set is 12

The standard deviation is 0.

This last one is really important, you can see that if we have at least one element different than the mean, then we will have at least one term different than zero in the standard deviation sum. Thus, the standard deviation can only be zero if all the elements of the set are the same element (thus, all the elements are equal to the mean).

Then the set is:

{12, 12, 12, 12, 12, 12, 12, 12, 12, 12}

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