Question

Find the following percentiles: 60th and 95th

Values 90, 90, 100, 110, 110, 110, 110, 110, 110, 120, 120, 130

Answer 1

Solution:

Given that,

Arranging Observations in the ascending order, We get :
90,90,100,110,110,110,110,110,110,120,120,130

Here, n = 12

P₆₀ = ( 60 ( n + 1 ) /100 )^th Value of Observations

   = ( 60 * 13/100 )^th Value of Observations

= 7.8^th  Value of Observations

=7^th Observations + 0.8^th ( 8^th - 7^th )

= 110 + 0.8 (110 - 110 )

= 110 +0.8 (0 )

= 110 + 0

= 110

P₆₀ = 110

P₉₅

Arranging Observations in the ascending order, We get :
90,90,100,110,110,110,110,110,110,120,120,130

Here, n=12

Since there are 12 values, then n=12.

Now, calculate the index i= p /100*n

= 95 /100*12 = 11.4.

Since index i is not an integer, round up: i = 12.

The percentile is at the position i=12: it is 130.

P₉₅ = 130