How is percentile calculated

Question

I have the following list: [1, 2, 6, 2, 2, 8, 8] and python gives me the following values for percentiles for each of the element:

[14.28, 42.85, 71.42, 42.85, 42.85, 92.85, 92.85]

Can anyone explain how to calculate them by hand?

Answer 1

Sort.

$1, \color{green}2, \color{green}2, \color{green}2, 6, \color{blue}8, \color{blue}8$

Take the ranks.

$1, \color{green}2, \color{green}3, \color{green}4, 5, \color{blue}6, \color{blue}7$

Average the ranks of equal elements.

$1, \color{green}3, \color{green}3, \color{green}3, 5, \color{blue}{6.5}, \color{blue}{6.5}$

In the original order.

$1, \color{green}3, 5, \color{green}3, \color{green}3, \color{blue}{6.5}, \color{blue}{6.5}$

Divide by 7 and express in percents.