Question

I am stuck on this question, I need to find the percentile.

Answer 1

`P_(26)\text{ = 5.46}`

Step-by-step explanation:

Arraging in ascending order:

6, 9, 14, 16, 31, 32, 37, 43, 45, 47, 53, 56, 62, 66, 71, 80, 82, 88, 92, 93, 95

The ranks of the numbers respectively is from:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21

We are to find the 26th percentile:

`\begin{gathered} Rank=(26)/(100)(number\text{ of rank)} \\ Rank=(26)/(100)(21\text{)} \\ \text{Rank = 5.46} \\ \text{whole number = 5, decimal number = 0.46} \end{gathered}`

We consider the whole number = 5

We find the numbers corresponding to rank 5 and 6

31 corresponds to 5 and 32 corresponds to 6

Then we find the product of the decimal and the differnce between the numbers in the ranks we got:

decimal = 0.46

difference = 32 - 31

`\begin{gathered} =\text{ (32 - 31) (0.46)} \\ =\text{ 0.46} \end{gathered}`
`\begin{gathered} P_(26)\text{ = }whole\text{ number + 0.46} \\ P_(26)\text{ = 5 + 0.46} \\ P_(26)\text{ = 5.46} \end{gathered}`