Question

The following data represent The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point?

Answer 1

Upper fence = Q3 + 1.5(IQR)

where

Q3 = third quartile

IQR = interquartile range = (Q3 - Q1)

Q1 = first quartile

The first step is to rearrange the data in ascending order. We have

340, 358, 359, 364, 367, 389, 403, 433, 471, 482, 486, 487, 488,488, 489, 489, 508, 512, 536, 537

Q1 is the median of the lower half of the data. From the calculator,

Q1 = 365.5

Q1 is the median of the upper half of the data

Q3 = (489 + 489)/2 = 489

IQR = 489 - 365.5 = 123.5

By substituting these values into the formula,

Upper fence = 489 + 1.5(123.5)

Upper fence = 674.25

Cut off point = 674.25