Question

Consider the following data set. 39 38 16 19 30 6 10 20 26 a​) Determine...

Consider the following data set.

39
38
16
19
30
6
10
20
26

a​) Determine the 15th percentile.

b​) Determine the 45th percentile.

c​) Determine the 85th percentile.

Homework Answers

Answer #1

Solution:
Arranging Observations in the ascending order, We get :
6,10,16,19,20,26,30,38,39

Here, n=9

a ) P15=(15(n+1)100)th value of the observation

=(15⋅10/100)th value of the observation

=(1.5)th value of the observation

=1st observation +0.5[2nd-1st]

=6+0.5[10-6]

=6+0.5(4)

=6+2

=8

b ) P45=(45(n+1)100)th value of the observation

=(45⋅10/100)th value of the observation

=(4.5)th value of the observation

=4th observation +0.5[5th-4th]

=19+0.5[20-19]

=19+0.5(1)

=19+0.5

=19.5

c ) P85=(85(n+1)100)th value of the observation

=(85⋅10/100)th value of the observation

=(8.5)th value of the observation

=8th observation +0.5[9th-8th]

=38+0.5[39-38]

=38+0.5(1)

=38+0.5

=38.5

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