[tex]P_{26}\text{ = 5.46}[/tex]
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:
[tex]\begin{gathered} Rank=\frac{26}{100}(number\text{ of rank)} \\ Rank=\frac{26}{100}(21\text{)} \\ \text{Rank = 5.46} \\ \text{whole number = 5, decimal number = 0.46} \end{gathered}[/tex]
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
[tex]\begin{gathered} =\text{ (32 - 31) (0.46)} \\ =\text{ 0.46} \end{gathered}[/tex][tex]\begin{gathered} P_{26}\text{ = }whole\text{ number + 0.46} \\ P_{26}\text{ = 5 + 0.46} \\ P_{26}\text{ = 5.46} \end{gathered}[/tex]
