Question

• Following is the travel time in minutes to work of the 20 New Yorkers. Calculate both the range and the IQR and interpret the value (what it means)
• 60, 65, 5, 10, 40, 10, 60, 45, 15, 15, 40, 15, 15, 20, 30, 20, 85, 20, 25, 30

Answer 1

Solution :

Arranging Observations in the ascending order,

5,10,10,15,15,15,15,20,20,20,25,30,30,40,40,45,60,60,65,85

Range = maximum - minimum = 85 - 5 = 80

Here, n=20

Q1 = (n+1 / 4)th value of the observation

= (21 / 4)th value of the observation

= (5.25)th value of the observation

= 5th observation + 0.25[6th - 5th]

=15 + 0.25[15 -15]

= 15 + 0.25(0)

=15 + 0

= 15

Q1 = 15

Q3 = (3(n+1)/ 4)th value of the observation

= (3⋅21 / 4)th value of the observation

= (15.75)th value of the observation

= 15th observation + 0.75[16th - 15th]

= 40 + 0.75[45 - 40]

= 40 + 0.75(5)

= 40 + 3.75

Q3 = 43.75

IQR = Q3 - Q1 = 43.75 - 15 = 28.75