Which of the following highest Standard deviation 7, - 7, 7,-7, 7,-7 b) 7, 7, 7,7,7,7 c) -7, - 7, -7,-7,-7,-7?

d) -7, 7, -7, 7,-7, 7





answer with explanation

Which of the following highest Standard deviation 7, - 7, 7,-7, 7,-7 b) 7, 7, 7,7,7,7 c) -7, - 7, -7,-7,-7,-7?
Your a) and d) look like they are just multiplied by -1 for each number.





If that's the case, then a) and d) would have the same standard deviation and it would be higher than b) or c) which have the same standard deviation of zero.





The reason is that standard deviation is a measure of probability of finding an occurance away from the mean. In the case of a) and d), the mean is zero. However, in 6 consecutive samples, you repeatedly found numbers 7 away from the mean on either side. So that says the distribution must be very wide for you to have the chance to repeatedly finding a number 7 from the mean. By contrast, you repeatedly found the same number for b) and c), each 6 times. That says the distribution must be very narrow around the mean in order for you to repeatedly find exactly the same numer.





If you really want to argue, by the way, you can argue that a) and d) appear more bimodal than normal. You shouldn't apply a normal statistics to a data sampling that is bimodal and therefore the question is meaningless. But I suspect that's beyond what the questioner is asking.
Reply:they are all the same...zero.
Reply:b because brilliant brains bomb butterflies before bedtime of course








hahahahahahhahha no actually im not kiddin
Reply:I'm a little confused, a) and d) look to have the same numbers. From what I can tell, however, the group of 7 -7 7 -7 7 -7 has the highest standard deviation. This is because a standard deviation is the standard distance a number in any data set is from the mean of the data. In b) and c), the numbers are all the same. So their mean is the same, and there is no distance between any of the values in the data set and the mean of the data.





For 7 -7 7 -7 7 -7 however, the mean is 0. So all of the values clearly have some space between them and the mean.





Check out this page on standard deviations:





http://www.gcseguide.co.uk/standard_devi...
Reply:A, the average would be zero, but D will give you the same answer. I hope that helps