Question

Calculate the 20th, 50th, and 80th percentiles for the following data set: (Use the methodology shown in Section 3.2 of the text to calculate the percentiles. Do not round intermediate calculations. Round your final answers to 1 decimal place.)

125 221 203 348 240 212 317

Answer 1

Solution:
Arranging Observations in the ascending order, We get :
125,203,212,221,240,317,348
Here, n = 7

P₂₀ = value of (20 (n + 1 ) / 100 )^th value of Observations

   =value of ((20 * 8 ) / 100 )^th value of Observations

= value of 1.6^th value of Observations

= 1^st Observations + 0.6 ( 2^nd - 1^st )

= 125 + 0.6 (203 - 125 )

= 125 + 0.6 ( 78 )

= 125 + 46.8

= 171.8

P₂₀ == 171.8

P₅₀ = value of (50 (n + 1 ) / 100 )^th value of Observations

   =value of ((50 * 8 ) / 100 )^th value of Observations

= value of 4^th value of Observations

= 221

P₅₀ = 221

P₈₀ = value of (80 (n + 1 ) / 100 )^th value of Observations

   =value of ((80 * 8 ) / 100 )^th value of Observations

= value of 6.04^th value of Observations

= 6^th Observations + 0.4 ( 7^th - 6^th )

= 317 + 0.4 (348- 317 )

= 317 + 0.4 ( 31 )

= 317 + 12.4

= 329.4

P₈₀ = 329.4