Question

The “1.5×IQR” rule states that a data value is potentially an outlier if its distance below the first quartile or above the third quartile is greater than 1.5 times the interquartile range.Which of the following box plots represents a data set with a potential outlier, as identified by the “1.5×IQR” rule? Select all that apply.

Answer 1

Using the 1.5×IQR Rule, all the box plots represent a data set that have a potential outlier.

What is the 1.5×IQR Rule?

This rule utilizes the quartiles and interquartile range (IQR) of a dataset to establish upper and lower fences, designating any data point outside these boundaries as an outlier; the upper fence is calculated as Q3 + 1.5(IQR), and the lower fence is calculated as Q1 - 1.5(IQR).

First box plot:

IQR = 40 - 25 = 15

Q3 + 1.5(IQR) = 40 + 1.5(15) = 62.5 [62.5 is beyond the threshold]

Q1 - 1.5(IQR) = 25 - 1.5(15) = 2.5

This box plot has a potential outlier.

Second box plot:

IQR = 35 - 20 = 15

Q3 + 1.5(IQR) = 35 + 1.5(15) = 57.5

Q1 - 1.5(IQR) = 20 - 1.5(15) = -2.5 [-2.5 is below the threshold]

This box plot has a potential outlier.

Third box plot:

IQR = 35 - 25 = 10

Q3 + 1.5(IQR) = 35 + 1.5(10) = 50

Q1 - 1.5(IQR) = 25 - 1.5(10) = 10 [10 is below the threshold]

This box plot has a potential outlier.

Fourth box plot:

IQR = 40 - 20 = 20

Q3 + 1.5(IQR) = 40 + 1.5(20) = 70 [70 is beyond the threshold]

Q1 - 1.5(IQR) = 40 - 1.5(20) = 10

This box plot has two potential outliers.

All the box plots have potential outlier.

Answer 2

Given:

“1.5×IQR” rule states that a data value is potentially an outlier if its distance below the first quartile or above the third quartile is greater than 1.5 times the interquartile range

Required:

To calculate Which of the following box plots represents a data set with a potential outlier, as identified by the “1.5×IQR” rule? Select all that apply.

Step-by-step explanation:

(1) Q1=25. Q3=35 IQR=35-25=10

Q1-1.5 IQR =10; Q3+1.5 IQR=50

The max is 55>50 (outlier)

(2) Q1=20 .Q3=40 =IQR=20

Q1-1.5 IQR =-10 Q3+1.5IQR=70

min=0>Q1-10; max=65<70 (No outlier)

(3) Q1=25.Q3=40 =IQR=15

Q1-1.5IQR=2.5; Q3+1.5 IQR=62.5

min=5>2.5 ; max=60<62.5 (No outlier)

(4)Q1=20.Q3=35 =IQR=15

Q1-1.5IQR=-2.5 ; Q3+1.5 IQR=57.5

max:60>57.5 (oulier)

Required answer:

Choose 1, 4