Question

Joi's friends jump as far as they can and record their results in inches. Their results include the observations 41, 37, 40, 39, 45, 34, 39, 42, and 41. Which number, if added to the dataset, would represent an outlier in the data?

Answer 1

First sort the data: 34, 37, 39, 39, 40, 41, 41, 42, 45.
Median = 40. Q1 = median of lower half = (37+39)/2 = 38. Q3 = median of upper half = (41+42)/2 = 41.5.
IQR = Q3 − Q1 = 41.5 − 38 = 3.5.
Outlier fences: Q1 − 1.5·IQR = 38 − 5.25 = 32.75, and Q3 + 1.5·IQR = 41.5 + 5.25 = 46.75.

So any added measurement < 32.75 or > 46.75 would be an outlier. As whole inches, for example 32 or 47 would be outliers. (Common single answer: 47.)