Step by step
The question
Question: find the 50th percentile of 3, 5, 6, 8, 9, 12 and 15.
The 50th percentile is a number with about 50% of the data below it.
50th percentile: about 50% 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: 50/100, times n plus 1.
n is how many numbers: 7.
i = 50100 × (n + 1)
50/100 is 0.5.
7 plus 1 is 8.
i = 0.5 × 8
0.5 times 8 is 4.
i = 4
Careful!
The rule uses n plus 1, not n.
Careful: times n + 1, not n
2 Count to the position
4 is a whole number.
We count to the 4th number: 8.
So the 50th percentile is 8.
P50 = 8
3 Check
Let's check: 3 of the 7 numbers are below 8.
That is about 43%, close to 50%.
So it makes sense!
below 8: 3 of 7 = 43% ≈ 50%
Let's look back.
First: find the position.
Then: count to the position.
Last: check.
Answer
P50 = 8