Question

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed.

Step 1:
Choose four numbers that have the smallest possible standard deviation. What is the numerical value of s in this case? Give your answer as a whole number (meaning no decimal places).

Step 2:
Is there more than one possibility for choosing four numbers that have the smallest possible standard deviation?

No.

Yes. Step 3: Choose four numbers that have the largest possible standard deviation. Match your choice of numbers below in rising order. Pay attention that the number 0 is the 11th choice. 1) 1 6) 6 11) 0 2) 2 7) 7 3) 3 8) 8 4) 4 9) 9 5) 5 10) 10 RN note, need extra care here on answer formatting. Enter the coded number of the term that corresponds to each choice: (That is, you are not entering the actual 4 values you have in mind but rather you enter the 4 codes values that match these values keeping in mind that for some reason this question has coded the value of zero as ‘11’. For example, if you thought a set of values of 0, 8, 9, 10 yielded the highest sd – for LaunchPad you would then submit the values ‘11’, ‘8’, ‘9’, ‘10’. First number (smallest). Second number. Third number. Fourth number (largest). Step 4: Is there more than one way to choose four numbers that give the largest possible standard deviation? Yes. No.

Answer 1

1. Standard deviation can be small (that is zero) if all the values in the sample are same. Hence, the 4 values can be

1,1,1,1

2. Yes

Yes, there are more than one possibility for choosing four numbers that have the smallest possible standard deviation. Until, all the 4 numbers are same the standard deviation will not change from 0. So, the 4 values can also be (0,0,0,0) or (2,2,2,2) or (3,3,3,3), etc.

3. Standard deviation will be large when the values are far from each other. In the given possible set 0 and 10 are the values wihch are far from each other than any other values. Hence, the possible 4 vlaues that could have larger standard deviation will be

0,0,10,10

The inputs for lanunchpad would look like

'11','11','10','10'

4. No

Standard deviation will be large when the values are far from each other. Since, there are 4 values, changing the value of one would also lead to smaller standard deviation than from the the 4 values of (0,0,10,10). Therefore, the only possible values are (0,0,10,10). There is no more than one way to choose four numbers that give the largest possible standard deviation.