Respuesta :
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:
[tex]P^{th}\text{ percentile = }\frac{(n+1)\text{.p}}{100}[/tex]Compute the 30th percentile as follows:
[tex]30^{th}\text{ percentile = }\frac{(17+1).30}{100}=\frac{18}{100}.30\approx5^{th\text{ }}Obs[/tex]The 5th observation from the arranged data set is 338 .
Thus, the 30th percentile is 338.
Compute the 75th percentile as follows:
[tex]75^{th}\text{ percentile = }\frac{(17+1).75}{100}\approx14^{th\text{ }}Obs[/tex]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
