Answer to Question #119036 in Statistics and Probability for Leo

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

with sample sizes up to 80, each score with z-score≥2.50 or z-score≤-2.50 should be identified as outliers.

z1=(x-μ)/σ= (148-128.5)/8.2=2.378

z2=(102-128.5)/8.2=-3.23, -3.23≤-2.5 - outlier

z3=(152-128.5)/8.2=2.86, 2.86≥2.50 - outlier

average of the extracted scores that are outliers - (102+152)/2=127