Question

The following are the annual salaries of 17 chief executive officers of major companies.here are salaries 84, 381, 542,338,542,338,224,248,495.676,767,405,271,723,814,428,452,1108,609(the salaries are written in thousands of dollars)find the30th and the 75th percentiles for the salaries

Answer 1

To determine the 30th and the 75th percentiles for the salaries:

The pth percentile is a data value such that at least p% of the data-set is less-than or equal to this data value and at least (100-p)% of the data-set are more-than or equal to this data value.

Arrange the data set in ascending order as follows:

84 ,224 , 248, 271, 338 , 381, 405 , 428, 452, 495 , 542, 609, 676 , 723 ,767 , 814, 1108

The formula to compute the position of the pth percentile is:

`P^(th)\text{ percentile = }\frac{(n+1)\text{.p}}{100}`

Compute the 30th percentile as follows:

`30^(th)\text{ percentile = }((17+1).30)/(100)=(18)/(100).30\approx5^{th\text{ }}Obs`

The 5th observation from the arranged data set is 338 .

Thus, the 30th percentile is 338.

Compute the 75th percentile as follows:

`75^(th)\text{ percentile = }((17+1).75)/(100)\approx14^{th\text{ }}Obs`

The 14th observation from the arranged data set is 814.

Thus, the 75th percentile is 814

Therefore the 30th percentile is 338 and the 75th percentile is 814