# Question: New Standard Deviation

## Comment on New Standard Deviation

### In this case, mean will

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.

### If the mean is greater than

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

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.

### The 5 numbers that I use in

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

### So SD is unaffected when the

So SD is unaffected when the same number is added or subtracted across the set, right? What if the number is multiplied by the same number? Will there be a change in SD?

### In general, if D = the

In general, if D = the standard deviation of a certain set of numbers, then:

- the standard deviation will still be D if we ADD the same number to every value in the set.
- the standard deviation will still be D if we SUBTRACT the same number from every value in the set.
- the standard deviation will kD if we MULTIPLY each value in the set by k.
- the standard deviation will D/k if we DIVIDE each value in the set by k.