Question

Find the value of the 30th percentile of the following set of data. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20

Answer 1

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Answer 2

Answer:

The value of the 30th percentile of the following set of data is 8.

Step-by-step explanation:

Given : Set of data : 18, 9, 7, 5, 11,7, 17, 20, 19, 2, 17, 12, 5,1, 13, 12, 11, 15, 16, 20

To find : The value of the 30th percentile of the following set of data ?

Solution :

First we 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}

Using percentile formula,

First we compute $L=\frac{k}{100}\times n$

Where, n is number of values n=20

k is the percentile in question k=30

Substitute the value in the formula,

$L=\frac{30}{100}\times 20$

$L=6$

The value of $k^{th}$ percentile is midway between the $L^{th}$ value and next value is

$P_{30}=\frac{L^{th}+(L+1)^{th}}{2}$

$P_{30}=\frac{6^{th}+(6+1)^{th}}{2}$

$P_{30}=\frac{6^{th}+7^{th}}{2}$

$P_{30}=\frac{7+9}{2}$

$P_{30}=\frac{16}{2}$

$P_{30}=8$

Therefore, The value of the 30th percentile of the following set of data is 8.