Question

Choose four numbers with the largest possible standard deviation. You may use the same number more than once. First number _ Second Number _ Third number _ Fourth Number _ Answer Bank 0,1,2,3,4,5 Now, Choose four numbers with the smallest possible standard deviation. You may use the same number more than once. First number _ Second Number _ Third number _ Fourth Number _ Answer Bank 0,1,2,3,4,5 Is you selection of numbers the only possible correct answer? Yes _ No_ (Please show work).

Answer 1

To find four numbers with the largest possible standard deviation from the set (0, 1, 2, 3, 4, 5), one could select 0, 0, 5, 5. For the smallest possible standard deviation, any number repeated four times, such as 1, 1, 1, 1, will do. There are multiple combinations that could result in these extremes of standard deviation.

Step-by-step explanation:

To choose four numbers with the largest possible standard deviation, we want to maximize the differences between the numbers. From the provided answer bank (0, 1, 2, 3, 4, 5), the numbers that are furthest apart are 0 and 5. Therefore, a set that maximizes the standard deviation could be 0, 0, 5, 5. This set has the largest range, which contributes to a larger standard deviation.

For the smallest possible standard deviation, it is ideal to select numbers that are as close to each other as possible. The best choice would be to pick the same number four times because the standard deviation of identical numbers is zero. We could choose any number from the answer bank and repeat it four times. For example, 1, 1, 1, 1 would result in the smallest standard deviation, which is zero.

Clearly, the selection of numbers for the largest standard deviation is not the only possible correct answer as you could also select 0, 5, 0, 5 or any combination where there are two 0s and two 5s. For the smallest standard deviation, any number repeated four times is also a correct answer.