Thursday

September 3, 2015
Posted by **statistics** on Tuesday, July 28, 2009 at 11:46am.

pick four numbers that would have the smallest standard deviation

I said four zeros

pick four numbers that would have the largest standard deviation

I said 0 0 0 10

is there more than one correct answer for either of these questions

- statistics -
**MathMate**, Tuesday, July 28, 2009 at 12:01pmStandard deviation σ is given by:

σ² = Σ (x-x̄)²/n

So if you can find the smallest difference between x and x̄, you have found the smallest value.

(0,0,0,0) would work as well as any other number such as (5,5,5,5).

For the maximum value, we would see the biggest spread possible. For four numbers, I would try (0,0,10,10). Try out other combinations (such as 0,0,0,10 and 0,10,10,10 to convince yourself that you have got the maximum.

- statistics -
**drwls**, Tuesday, July 28, 2009 at 12:02pmAny four numbers that are the same would have a standard deviation of zero.

The set of numbers 0,0,10,10 would have the largest average deviation from the mean (5). I suspect that would also have the largest standard deviation (also 5). Try others and see