Consider a sample with data values of 29, 27, 22, 17, 32, 38, 30, and 27. Compute the 20th, 25th, 65th, and 75th percentiles.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
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Consider a sample with data values of 29, 27, 22, 17, 32, 38, 30, and 27. Compute the 20th, 25th, 65th, and 75th percentiles.
Step 1
Recall that a percentile gives insight to how data are spread between the smallest and largest values. The pth percentile of a set of data indicates that p% of the data are below that value, and 
(100 − p)%
 are above that value. There are two components of the pth percentile: the location within the data and the actual value.
The formula for finding the location of the percentile, denoted Lp, follows where p is the percentile and n is the number of observations in the ordered data set.
Lp = 
p
100
(n + 1)
The first step in calculating a percentile is to order the data in ascending order. The ordered data are below.
17 22 27 27 29 30 32 38
There are 
n = 8
 observations in the data. Find the location of the p = 20th percentile.
Lp  = 
p
100
(n + 1)
L20  = 
20
100
 
  + 1
 
 
   =   
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