Question

Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find P10. 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

Answer 1

Answer:

$P_{10} =0.1$

Explanation:

Given

$0.1, 0.1, 0.3, 0.3, 0.3, 0.4, 0.4, 0.4, 0.6, 0.7, 0.7, 0.7, 0.8, 0.8$

Required

Determine $P_{10}$

$P_{10}$ implies 10th percentile and this is calculated as thus

$P_{10} = \frac{10(n+1)}{100}$

Where n is the number of data; n = 14

$P_{10} = \frac{10(n+1)}{100}$

Substitute 14 for n

$P_{10} = \frac{10(14+1)}{100}$

$P_{10} = \frac{10(15)}{100}$

Open the bracket

$P_{10} = \frac{10 * 15}{100}$

$P_{10} = \frac{150}{100}$

$P_{10} = 1.5th\ item$

This means that the 1.5th item is $P_{10}$

And this falls between the 1st and 2nd item and is calculated as thus;

$P_{10} = 1.5th\ item$

Express 1.5 as 1 + 0.5

$P_{10} = (1 +0.5)\ th\ item$

$P_{10} = 1^{st}\ item +0.5(2^{nd} - 1^{st}) item$

From the given data; $1st\ item = 0.1$ and $2nd\ item = 0.1$

$P_{10} = 1^{st}\ item +0.5(2^{nd} - 1^{st}) item$ becomes

$P_{10} =0.1 +0.5(0.1 - 0.1)$

$P_{10} =0.1 +0.5(0)$

$P_{10} =0.1 +0$

$P_{10} =0.1$