This is a standard deviation c
This is a standard deviation contest. You must choose fournumbers from the whole numbers 0 to 10, with repeats allowed.Step 1:Choose four numbers that have the smallest possible standarddeviation. What is the numerical value of s in this case? Give youranswer as a whole number (meaning no decimal places).
Step 2:Is there more than one possibility for choosing four numbers thathave the smallest possible standard deviation?
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Answer:
1. Standard deviation can be small (that is zero) if all thevalues 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 fournumbers that have the smallest possible standard deviation. Until,all the 4 numbers are same the standard deviation will not changefrom 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 fromeach other. In the given possible set 0 and 10 are the values wihchare far from each other than any other values. Hence, the possible4 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 fromeach other. Since, there are 4 values, changing the value of onewould also lead to smaller standard deviation than from the the 4values of (0,0,10,10). Therefore, the only possible values are(0,0,10,10). There is no more than one way tochoose four numbers that give the largest possible standarddeviation.
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