Answer to Question #119273 in Statistics and Probability for Augustine

Question

The average mark of candidates in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the extracted scores that are extreme values (outliers)?

Answer 1

$\text{According to the Empirical rule any}\\ \text{ value outside two standard deviations}\\ \text{ِ of the mean is considered an outlier}\\ upper\; limit=128.5+2(8.2)=144.9,\\ lower \;limit=128.5-2(8.2)=112.1\\ \text{the range of two standard deviation}\\ \text{ of the mean is (112.1,144.9)}\\ \text{So all the values are outliers}\\ \text{the average of the extracted scores that }\\ \text{are extreme values (outliers)} \\=\frac{148+102+152}{3}=134$