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

Question

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

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

Answers

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


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