Find the values of the 40th and 90th percentile of the data

Question

Find the values of the 40th and 90th percentile of the data

25,1,6,17,20,9,12,18,5,3,11,19,24,5,12,19,23,20,2,10

Answer 1

Here's the procedure.

1. Put the data in order (smallest to largest)
2. Find the median (μ)
3. Use your calculator to find the standard deviation (σ) of the data set
4. Find the 40th percentile (number closest to 0.40) in a z-score table (http://www.z-table.com/) and record the z-score, which is -1.75.  To find the data item that correspond to the 40th percentile, use the z-score formula and solve for x (the data item):

 

        z = (x-μ)/σ

       -1.75 = (x-μ)/σ

       (-1.75)σ = x-μ

       (-1.75)σ + μ = x

 

Plug in the values of μ and σ you determined in steps 2 and 3 and compute the value of x.  Find the value of the data that is closest to x.  That is the 40th percentile.  Repeat step 4 for the 90th percentile (find the z-score closest to 0.90).