Problem 7E

Is it possible for the standard deviation of a list of numbers to equal 0? If so, give an example. If not, explain why not.

Solution 7E

Step1 of 3:

In a given problem they told that to take list of same numbers.

We need to check whether the standard deviation to be Zero for the list of same numbers. If yes, we have to give Example.

Step2 of 3:

“Yes”, for the given list of positive numbers standard deviation Zero.

Example:

Let us consider X be random variable and it has 3 samples(that is 3 positive numbers).

X = 2, 2, 2.

1).Mean of the X is given by:

Where,

= Mean

x = random variable

N = sample size

= 3.

Now,

=

=

= 2

Therefore, = 2.

Step3 of 3:

2).Standard deviation of X is given by:

=

=

=

=

=

= 0

Hence, = 0.

Conclusion:

Therefore, For the given list of positive numbers standard deviation is Zero.