Answer:
[tex]P_{10} =0.1[/tex]
Explanation:
Given
[tex]0.1, 0.1, 0.3, 0.3, 0.3, 0.4, 0.4, 0.4, 0.6, 0.7, 0.7, 0.7, 0.8, 0.8[/tex]
Required
Determine [tex]P_{10}[/tex]
[tex]P_{10}[/tex] implies 10th percentile and this is calculated as thus
[tex]P_{10} = \frac{10(n+1)}{100}[/tex]
Where n is the number of data; n = 14
[tex]P_{10} = \frac{10(n+1)}{100}[/tex]
Substitute 14 for n
[tex]P_{10} = \frac{10(14+1)}{100}[/tex]
[tex]P_{10} = \frac{10(15)}{100}[/tex]
Open the bracket
[tex]P_{10} = \frac{10 * 15}{100}[/tex]
[tex]P_{10} = \frac{150}{100}[/tex]
[tex]P_{10} = 1.5th\ item[/tex]
This means that the 1.5th item is [tex]P_{10}[/tex]
And this falls between the 1st and 2nd item and is calculated as thus;
[tex]P_{10} = 1.5th\ item[/tex]
Express 1.5 as 1 + 0.5
[tex]P_{10} = (1 +0.5)\ th\ item[/tex]
[tex]P_{10} = 1^{st}\ item +0.5(2^{nd} - 1^{st}) item[/tex]
From the given data; [tex]1st\ item = 0.1[/tex] and [tex]2nd\ item = 0.1[/tex]
[tex]P_{10} = 1^{st}\ item +0.5(2^{nd} - 1^{st}) item[/tex] becomes
[tex]P_{10} =0.1 +0.5(0.1 - 0.1)[/tex]
[tex]P_{10} =0.1 +0.5(0)[/tex]
[tex]P_{10} =0.1 +0[/tex]
[tex]P_{10} =0.1[/tex]
