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 to the extracted scores that are extreme values(outliers)

Answer 1

$Z=\frac{x- \mu}{\sigma}\\ Z_{1}=\frac{148- 128.5}{8.2}=2.38\\ Z_{2}=\frac{102- 128.5}{8.2}=-3.23\\ Z_{3}=\frac{152- 128.5}{8.2}=2.86\\ \text{We can treat any data value with a z-score less}\\ \text{ than -2 or greater than 2 as an outlier}\\ \text{ so all of them are outliers.}\\ \text{the average of the extracted scores that }\\ \text{are extreme values (outliers)} \\=\frac{148+102+152}{3}=134$