Step by step
The question
Question: find the first quartile, Q1, of 4, 6, 7, 9, 12, 13 and 15.
Q1 is the 25th percentile.
About 25% of the numbers are below it.
Q1 = the 25th percentile: about 25% 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: 25/100, times n plus 1.
n is how many numbers: 7.
i = 25100 × (n + 1)
25/100 is 0.25.
7 plus 1 is 8.
i = 0.25 × 8
0.25 times 8 is 2.
i = 2
Careful!
The rule uses n plus 1, not n.
Careful: times n + 1, not n
2 Count to the position
2 is a whole number.
We count to the 2nd number: 6.
So the Q1 is 6.
Q1 = 6
3 Check
Let's check: 1 of the 7 numbers are below 6.
That is about 14%, close to 25%.
So it makes sense!
below 6: 1 of 7 = 14% ≈ 25%
Let's look back.
First: find the position.
Then: count to the position.
Last: check.
Answer
Q1 = 6