Question

Chapter 2, Section 4, Exercise 138a Incorrect The following describes a sample. The information given includes the five number summary, the sample size, and the largest and smallest data values in the tails of the distribution. Five number summary: (13,40,50, 54,69); Tails: 13, 18, 26,28,29,.., ,62,63, 63,64, 69 120 Clearly identify any outliers using the IQR method. Select all that apply. No outliers O 13 18 O 26 O 28 29 O 62 O 63 O 63 O 64 69

Answer 1

Given five number summary is, (13, 40, 50, 54, 69)

where, minimum value = 13, first quartile (Q₁) = 40,

second quartile = median (Q₂) = 50, third quartile (Q₃) = 54,

maximum value = 69

IQR = Q₃ - Q₁ = 54 - 40 = 14

1.5 * IQR = 1.5 * 14 = 21

To determine if there are outliers we must consider the numbers that are 1.5·IQR or 21 beyond the quartiles.

first quartile – 1.5·IQR = 40 - 21 = 19
third quartile + 1.5·IQR = 54 + 21 = 75

Since the data values 13 and 18 are outside the interval from 19 to 75.

Hence, outliers are 13 and 18