Question: Ordering Standard Deviations

Comment on Ordering Standard Deviations

Hello. In Data Set II, I see how you got the average, however, when I was doing this I had 10 because I thought with an odd number of numbers, the median=mean.
greenlight-admin's picture

Median = mean when all of the values in a set are equally spaced.

If there is an odd number of values, the median is the middlemost value, but we can't make any conclusions about the mean.

Here's the video on when the median = the mean:

Is it possible for range to also infer which is the greater S.D.
For example,the higher the range,the higher the S.D.
II has the highest S.D because it has a range of 3 followed by III which has a range of 2 then finally I because it has range of 0.2.
greenlight-admin's picture

Sometimes the set with the greatest range will also be the set with the greatest Standard Deviation, but this isn't always the case.

Consider these two sets:
Set A: {0, 5, 5, 5, 5, 5, 5, 5, 10}
Set B: {0, 0, 0, 0, 4, 8, 8, 8, 8}

Set A has a mean of 5.
Notice that 7 of the values in set A are equal to the mean.
The remaining values (0 and 10) are each 5 units from the mean

Set B has a mean of 4.
Notice that only 1 value in set B is equal to the mean.
The remaining values (0, 0, 0, 0, 8, 8, 8 and 8) are each 4 units from the mean

If we think about Standard Deviation as the average distance from the mean, we can see that the Standard Deviation of Set B is greater than the Standard Deviation of Set A, EVEN THOUGH the range of Set A is greater than the range of Set B.

Does that help?


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