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?

315

300

140

165

Solution

, IQR = Q₃ - Q_{1 = 260 - 220 = 40}

h = 1.5IQR = h = 1.5*40 = 60

LIF = Q1 - h = 220 - 60 = 160

UIF = Q3+h = 260+60 = 320

Points beyond these fences are potential outliers. Those points of the data set which are closest to the fences but still inside the fences are called the adjacent points . Therefore the adjacent point is 315

315