Question

11. In a boys’ school, there are 45 students in grade 10. The height of the students was measured. The mean height of the students was 154 cm and the standard deviation was 2 cm. Alex’s height was 163 cm. Would his height be considered an outlier, if the height of the students were normally distributed? Explain your answer.

Answer 1

Alex's z-score: $z=\frac{163-154}{2}=4.5$.

A standard cut-off value for finding outliers are Z-scores of +/-3 or further from zero.

Since 4.5>3, the Alex's height is an outlier.