Worked examples
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.
▶ Watch it solved
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.
▶ Watch it solved
The question
Question: find the first quartile, Q1, of 3, 7, 8, 5, 12, 14, 21, 13, 18, 6 and 9.
Q1 is the 25th percentile.
About 25% of the numbers are below it.
Q1 = the 25th percentile: about 25% are below it
1 Put them in order
In order, smallest to biggest.
Small green numbers count the positions: 1, 2, 3, and so on.
2 Find the position
The position i: 25/100, times n plus 1.
n is how many numbers: 11.
i = 25100 × (n + 1)
25/100 is 0.25.
11 plus 1 is 12.
i = 0.25 × 12
0.25 times 12 is 3.
i = 3
Careful!
The rule uses n plus 1, not n.
Careful: times n + 1, not n
3 Count to the position
3 is a whole number.
We count to the 3rd number: 6.
So the Q1 is 6.
Q1 = 6
4 Check
Let's check: 2 of the 11 numbers are below 6.
That is about 18%, close to 25%.
So it makes sense!
below 6: 2 of 11 = 18% ≈ 25%
Let's look back.
First: put them in order.
Then: find the position.
Then: count to the position.
Last: check.
▶ Watch it solved
