Question

Consider the data set

1.5	7.0	8.2	8.7
2.9	7.0	8.2	8.8
4.9	7.6	8.5	9.2
6.5	7.7	8.5	9.3
6.9	8.0	8.5	9.6

Which data point is the 95th percentile?

Answer 1

Solution:

Given that,
Arranging Observations in the ascending order, We get :
1.5,2.9,4.9,6.5,6.9,7,7,7.6,7.7,8,8.2,8.2,8.5,8.5,8.5,8.7,8.8,9.2,9.3,9.6

Here, n = 20

P₉₅ = ( 95(n + 1 ) / 100 )^th Value of observation

  = ( 95 * 21 / 100 )^th Value of observation

= ( 19.95)^th​​​​​​​ Value of observation

= 19^th​​​​​​​ observation + 0.95 (20^th​​​​​​​ - 19^th​​​​​​​ )

   = 9.3 + 0.95 (9.3​​​​​​​ - 9.6​​​​​​ )

= 9.3 + 0.95 (0.3 )

= 9.3 + 0.285

= 9.585.

P₉₅  ​​​​​​​= 9.585