Question

The standard deviation of a dataset was 6. However, it was later found that this dataset contained 2 outliers. So, they were removed, the standard deviation was calculated again as s. Which of the following is true?

(a) s < 6

(b) s > 6

(c) s = 6

(d) Not enough information

Answer 1

we know that when there is an outlier, then the standard deviation increases as the difference between data values increases

and when the outlier is removed, then the standard deviation decreases as the difference between data values decreases

So, in this case when outlier is removed, then standard deviation must be decreased or less than 6 because the difference between the data values must be decreased after removing the outlier

therefore, option A is correct