Step by step
The question
Question: find the 70th percentile of 18, 21, 22, 25, 26, 27, 29, 30, 31, 33, 36, 37, 41, 42, 47, 52, 55, 57 and 58.
The 70th percentile is a number with about 70% of the data below it.
70th percentile: about 70% 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: 70/100, times n plus 1.
n is how many numbers: 19.
i = 70100 × (n + 1)
70/100 is 0.7.
19 plus 1 is 20.
i = 0.7 × 20
0.7 times 20 is 14.
i = 14
Careful!
The rule uses n plus 1, not n.
That keeps the middle in the middle.
Careful: not 0.7 × 19 ✗
2 Count to the position
14 is a whole number.
We count to the 14th number: 42.
So the 70th percentile is 42.
P70 = 42
3 Check
Let's check: 13 of the 19 numbers are below 42.
That is about 68%, close to 70%.
So it makes sense!
below 42: 13 of 19 = 68% ≈ 70%
Let's look back.
First: find the position.
Then: count to the position.
Last: check.
Answer
P70 = 42