Suppose that you had the following data set. 500 200 250 275 300 suppose that the value 500 was a typo, and it was suppose to be negative (-500). how would the value of the standard deviation change?

The absolute difference is:

If we find the % of change respect the before case we have this:

So then is a big change.

Step-by-step explanation:

The subindex B is for the before case and the subindex A is for the after case

Before case (with 500)

For this case we have the following dataset:

500 200 250 275 300

We can calculate the mean with the following formula:

And the sample deviation with the following formula:

After case (With -500 instead of 500)

For this case we have the following dataset:

-500 200 250 275 300

We can calculate the mean with the following formula:

And the sample deviation with the following formula:

And as we can see we have a significant change between the two values for the two cases.

The absolute difference is:

If we find the % of change respect the before case we have this:

So then is a big change.