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

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.

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