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

`P_(10) =0.1`

Step-by-step 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) = (10(n+1))/(100)`

Where n is the number of data; n = 14

`P_(10) = (10(n+1))/(100)`

Substitute 14 for n

`P_(10) = (10(14+1))/(100)`

`P_(10) = (10(15))/(100)`

Open the bracket

`P_(10) = (10 * 15)/(100)`

`P_(10) = (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`