Question: New Standard Deviation

Comment on New Standard Deviation

In this case, mean will increase more than median depending on K value. But SD will remain constant.

even if we subtract the uniform value to all element, after also SD will remain same, mean and median would be decreasing, still mean will be more than median, right?

This wouldn't obviously be same if we add or subtract different value to different element of set.

seems like understanding this property is very helpful? please correct me if anything wrong.
greenlight-admin's picture

If the mean is greater than the median in a certain set, then if we subtract the same amount from each element in the set, the new set will be such that the mean is still greater than the median.

Similarly, if the mean is greater than the median in a certain set, then if we add the same amount from each element in the set, the new set will be such that the mean is still greater than the median.

And so on...

the question said, set x consist of 10 numbers and a mean of M, but your explanation is concluding that, the mean is 10 and instead of the set being 10 you made it 5 to answer the question. Can you please highlight on this for me.
greenlight-admin's picture

The 5 numbers that I use in the solution (qt 0:25 in the video) are meant to illustrate a point, not to represent the 10 numbers in the set.

The idea here is that adding the same value to ALL members in a set does not change the standard deviation.

For example, if we take the set {1, 2, 11, 20} and add 1 to every value, we get the set {2, 3, 12, 21}

These two sets {1, 2, 11, 20} and {2, 3, 12, 21} have the exact same standard deviation.

Likewise, if we take the set {1, 2, 11, 20} and add 5 to every value, we get the set {6, 7, 16, 25}, and these two sets have the exact same standard deviation.

So, although I used a set with 5 numbers to illustrate my point, we can extend this concept to ALL sets.

Does that help?

Cheers,
Brent

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