Step by step
The question
Question: find the 75th percentile of 10, 12, 15, 16, 18, 20 and 23.
The 75th percentile is a number with about 75% of the data below it.
75th percentile: about 75% are below it
They are already in order.
Small green numbers count the positions: 1, 2, 3, and so on.
1 Find the position
The position i: 75/100, times n plus 1.
n is how many numbers: 7.
i = 75100 × (n + 1)
75/100 is 0.75.
7 plus 1 is 8.
i = 0.75 × 8
0.75 times 8 is 6.
i = 6
Careful!
The rule uses n plus 1, not n.
That keeps the middle in the middle.
Careful: not 0.75 × 7 ✗
2 Count to the position
6 is a whole number.
We count to the 6th number: 20.
So the 75th percentile is 20.
P75 = 20
3 Check
Let's check: 5 of the 7 numbers are below 20.
That is about 71%, close to 75%.
So it makes sense!
below 20: 5 of 7 = 71% ≈ 75%
Let's look back.
First: find the position.
Then: count to the position.
Last: check.
Answer
P75 = 20