If the six entries have a mean of 5, what then must be their sum?
Square the standard deviation to get the value of the variance, and then use the alternative formula displayed here
. From the first calculation above, you can substitute for the sum of the values xi
. Using this, you can solve for the value of the sum of the squares.
Now pick values that have the appropriate sum, and see what is the sum of their squares. Make adjustments, as necessary, until you arrive at a set of values which works. (I believe there can be more than one "right" answer to this exercise.)