Question

The following data give the speeds (in miles per hour) of 12 cars traveling on a highway.

67 71 57 54 69 74 77 62 61 59 58 63

a. Calculate the values of three quartiles.

b. Find the (approximate) value of the 40th percentile.

c. Find the percentile rank of 62

Answer 1

Solution:
Arranging Observations in the ascending order, We get :
54,57,58,59,61,62,63,67,69,71,74,77

Here, n=12

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

=(3⋅13/4)th value of the observation

=(9.75)th value of the observation

=9th observation +0.75[10th-9th]

=69+0.75[71-69]

=69+0.75(2)

=69+1.5

=70.5

P40=(40(n+1)100)th value of the observation

=(40⋅13/100)th value of the observation

=(5.2)th value of the observation

=5th observation +0.2[6th-5th]

=61+0.2[62-61]

=61+0.2(1)

=61+0.2

=61.2

P62=(62(n+1)100)th value of the observation

=(62⋅13/100)th value of the observation

=(8.06)th value of the observation

=8th observation +0.06[9th-8th]

=67+0.06[69-67]

=67+0.06(2)

=67+0.12

=67.12