What is the value of the 30th percentile of the set of data: #18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20#?

Question

Emery Adams · Accepted Answer

#30th# percentile is #6th# item i.e. #7#

To calculate the percentile of a data set, we should first order all the values in the data set from smallest to largest.

The data now looks like #{1,2,5,5,7,7,9,11,11,12,12,13,15,16,17,17,18,19,20,20}#

As their are #20# data points and #30%# of this is #20xx30/100=6#.

Hence #30th# percentile is #6th# item i.e. #7#

Jameson Adams · Answer

undefined To find the 30th percentile of the given data set, first, arrange the data in ascending order:

1, 2, 5, 5, 7, 7, 9, 11, 11, 12, 12, 13, 15, 16, 17, 17, 18, 19, 20, 20

There are 20 data points in the set. To find the position of the 30th percentile, calculate:

$ \text{Position} = \frac{30}{100} \times 20 = 6 $

The 30th percentile falls between the 6th and 7th data points. To find the value, take the average of these two values:

$ \text{Average} = \frac{7 + 9}{2} = 8 $

So, the 30th percentile of the data set is 8.