Question

The work experiences (in years) of 14 employees of a company are 8 21 11 4 14 17 11 8 8 7 2 11 27 6

a) find the approximate value of the 70th percentile for these data.

b) the percentile rank for the employee with 17 years of experience is:

A) 62.96% B) 78.57% C) 68%   

Answer 1

Solution:

Given that,

a ) The 70th percentile is P₇₀

Arranging Observations in the ascending order, We get :

2,4,6,7,8,8,8,11,11,11,14,17,21,27

Here, n = 14

P₇₀ = ( 70 n + 1 / 100 )^th  value of the observation

  = ( 70 * 15 / 100 )^th  value of the observation

  = (10.5 )^th  value of the observation

    = (10 )^th  value of the observation + 0.5 ( 11^th - 10^th )

= 11 + 0.5 ( 14 - 11 )

= 11 +0.5 ( 3 )

= 11 + 1.5

= 12.5

P₇₀ = 12.5

b ) The percentile rank  

8 ,21, 11, 4 ,14, 17, 11, 8, 8, 7, 2 ,11, 27,6 = 14

Let k be the number of values in the dataset that are less than X = 17 . In this case, k = 11 k = 11 Hence, the percentile rank is

= k / n

= 11 /14

= 0.7857

= 78.57%

The percentile rank is 7857%

Answer B is correct.