A quantitative variable has the following five number summar

A quantitative variable has the following five number summary:

Min = 50 , Q1 = 220 , Median = 245 , Q3 = 260 , Max = 340

Which of the following observations would be denoted as an outlier in the boxplot for this variable?

180

325

165

300

Solution

The IQR is the length of the box in your box-and-whisker plot. An outlier is any value that lies more than one and a half times the length of the box from either end of the box. That is, if a data point is below Q₁ – 1.5×IQR or above Q₃ + 1.5×IQR, it is viewed as being too far from the central values to be reasonable

IQR = 260 - 220 = 40

Outliers will be any points below Q₁ – 1.5×IQR = 220 – 60 = 160 or above Q₃ + 1.5×IQR = 260 + 60 = 320

Then the outlier is

b.

325