using the numbers only 0 through 10 only whole numbers with repeats allowed
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
Standard 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.
Any 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
In both cases, there can be multiple correct answers.
To find the four numbers with the smallest standard deviation, we are looking for a set of numbers that are relatively close to each other. Since we are only allowed to use the numbers 0 through 10 with repeats allowed, one possible answer is to use four 0s (0, 0, 0, 0). However, another possible answer could be four 5s (5, 5, 5, 5) or four 10s (10, 10, 10, 10). In fact, any set of four identical numbers would have the smallest standard deviation.
To find the four numbers with the largest standard deviation, we are looking for a set of numbers that are spread apart from each other. One possible answer could be to use one 0 and three 10s (0, 10, 10, 10). However, another possible answer could be to use one 5 and three 10s (5, 10, 10, 10) or any combination of one smaller number and three larger numbers. The key is to have a significant difference between the numbers to maximize the standard deviation.
Therefore, both questions allow for multiple correct answers depending on the choice of numbers within the given range.