Question

Fill in the table Ch.2

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 63rd, and 73rd percentiles. If needed, round your answers to two decimal digits.

Percentile	Value
20%
25%
63%
73%

Answer 1

Solution:
Arranging Observations in the ascending order, We get :
15,20,25,25,27,28,30,34

Here, n=8

P20=(20(n+1)100)th value of the observation

=(20⋅9100)th value of the observation

=(1.8)th value of the observation

=1st observation +0.8[2nd-1st]

=15+0.8[20-15]

=15+0.8(5)

=15+4

=19

20th percentiles =19

P25=(25(n+1)100)th value of the observation

=(25⋅9100)th value of the observation

=(2.25)th value of the observation

=2nd observation +0.25[3rd-2nd]

=20+0.25[25-20]

=20+0.25(5)

=20+1.25

=21.25
25th percentiles =21.25

P63=(63(n+1)100)th value of the observation

=(63⋅9100)th value of the observation

=(5.67)th value of the observation

=5th observation +0.67[6th-5th]

=27+0.67[28-27]

=27+0.67(1)

=27+0.67

=27.67

63rd percentiles =27.67

P73=(73(n+1)100)th value of the observation

=(73⋅9100)th value of the observation

=(6.57)th value of the observation

=6th observation +0.57[7th-6th]

=28+0.57[30-28]

=28+0.57(2)

=28+1.14

=29.14

73rd percentiles=29.14