Step by step
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.
Answer
Q1 = 6