Standard deviation problem......??

can anyone tell the answer and the method to solve the below problem .......... is there any shortrick to solve them......??








1)Which of the following set of numbers has the highest Standard deviation?


a)1,0,1,0,1,0 b)-1,-1,-1,-1,-1,-1 c)1,1,1,1,1,1 d)1,1,0,-1,0,-1








2. which of the follwing group has highest standard deviation?


1) 2, 0, -2, 2, 0, -2


2) 2, 2, 2, 2, 2, 2


3) -2, -2, -2, -2, -2, -2


4) 2, -2, 2, -2, 2, -2

Standard deviation problem......??
Standard deviation is basically a measure of how much of a difference there normally is between different measurements in your set. If you have a set like {1,5,8,3,10,5,12,-2,21}, your standard deviation is relatively large because your numbers are all over the place. If you have a set like {5,6,4,5,7,5,4,5,5,6}, your standard deviation is pretty small because most of your numbers are pretty close together.





For problem 1:


a) This set has different numbers with a small difference, so there is a standard deviation.


b) All the numbers are the same, so the standard deviation is 0.


c) Again, all the numbers are the same, so the standard deviation is 0.


d) The numbers range from -1 to 1, which is the biggest range among all of your sets. Clearly, this standard deviation is higher than (a).





So, the answer is (d).








Problem 2:


Based on the same reasoning, you can eliminate choices (2) and (3) because those standard deviations are both equal to zero.


Between choices 1 and 4, you can decide based purely on the fact that choice 1 also has the 0 in between. Because of this, you have more numbers that are closer to the average of the set (the average of both sets is 0). Nevertheless, you could also just calculate the standard deviation for those last two if you want to check your answer... the st. dev. values for choices 1 and 4 are actually fairly close to each other.





So, the answer is (4).








EDIT: FYI, The person who answered after me is wrong; don't use that answer. The mean of {1,0,1,0,1,0} is 0.5, not 7. The standard deviation is 0.55, not 8. How can the mean of 1's and 0's be equal to 7?


I don't mean any offense, I just want to make sure that you don't use the wrong answer.
Reply:A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean


sooo....


{1,0,1,0,1,0} has a mean of 7 so standard deviation = 8.0829


{-1,-1,-1,-1,-1,-1} has a mean of -1 so standard deviation = 0


{1,1,1,1,1,1} has a mean of 1 so standard deviation also = 0


{1,1,0,-1,0,-1} has a mean of 0 so standard deviation = 0.89443


now... since you are looking for the "Highest" Standard Deviation, the answer must be 8.0829





That was the answer to number 1.





Here goes number 2.





{2, 0, -2, 2, 0, -2} has a mean of 0 and standard deviation = 1.78885


{2, 2, 2, 2, 2, 2} has a mean of 2 and standard deviation = 0


{-2, -2, -2, -2, -2, -2} has a mean of -2 and standard deviation also = 0


{2, -2, 2, -2, 2, -2} has a mean of 0 and the standard deviation = 2.19089





So, in your case, the highest "Standard Deviation" must be 2.19089





I Hope this helped you. I am pretty sure it is correct, but if it isn't good luck lol.





I have also put a source that should give you some assistance for further problems if needed.
Reply:1) a


2) 4

phlox