Question 721145: Compute the mean, range, and standard deviation for the data items in each of the three samples. Then name one way in which the samples are alike and one way in which they are different.
Sample A: 12,14,16,18,20,22,24
Sample B: 12,15,15,18,21,21,24
Sample C: 12,12,12,18,24,24,24
Answer by Positive_EV(69)   (Show Source):
You can put this solution on YOUR website! The mean of a distribution is the sum of its values over the number of values. I'll leave the calculation to this but, in the most astonishing and probably not intended at all by your instructor coincidence ever, the mean for every distribution is 18.
The range of a distribution is the difference between its highest value and its lowest value. Every distribution has a high value of 24 and a low value of 12, so the range of each distribution is (24-12) = 12.
Each distribution is different, but has the same mean and range. Let's try to find something that makes these distributions different. The standard deviation of a distribution can be calculated as either
 or 
Because this is a sample and not a census, you'd prefer the former formula. Again, this can be done by hand, but seriously who has time for that?
SD(A): 4.32049
SD(B): 4.24264
SD(C): Exactly 6
So, the similarities between the distributions are:
All have 7 observations
All have a median of 18
All of a mean of 18
All have a range of 12
All data sets are completely unskewed (that is, they are all symmetric about their mean/median)
The differences are:
All have a different standard deviation. B's data are the least spread out, then A's, then C's.
All have different modes (A has no mode, B has 15 and 21 as modes, C has 12 and 24 as modes).
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