Answer to Question #350464 in Statistics and Probability for sandy

Question

The mean of a normally distributed data is 23.6 with a standard deviation of 4.4. Which of the following scores is considered to be an extreme outlier?

Answer 1

A common method to define outliers is the “3 times the standard deviation” rule, referred to as the three-sigma rule of thumb.

The data lying less than -3sigma from the mean, and greater than 3sigma from the mean can be removed from the dataset.

$$\mu-3\sigma=23.6-3(4.4)=10.4$$

$$\mu+3\sigma=23.6+3(4.4)=36.8$$

The data less than 10.4 or greater 36.8 are outliers.