Step by step
The question
Question: draw a box plot of 3, 9, 4, 7, 15, 6, 8, 5 and 11.
A box plot shows how the numbers spread out.
The box holds the middle half.
1 Put them in order
First we put them in order, smallest first: 3, 4, 5, 6, 7, 8, 9, 11 and 15.
2 Find the median
9 numbers: 4 on each side of the middle one.
The median is 7.
3 Find Q1 and Q3
The median cuts the list in two halves, 4 numbers each.
The median itself is in neither half.
Careful!
The median is not counted in the halves.
Each half has 4 numbers.
The lower half has two in the middle: 4 and 5.
Q1 is halfway between them: we add them and divide by 2.
4 plus 5 is 9.
Divided by 2 is 4.5.
The upper half has two in the middle: 9 and 11.
Q3 is halfway between them: we add them and divide by 2.
9 plus 11 is 20.
Divided by 2 is 10.
4 Five-number summary
The five-number summary: the smallest 3, Q1 4.5, the median 7, Q3 10, and the biggest 15.
5 Draw the box plot
A number line from 3 to 15.
The box goes from Q1, 4.5, to Q3, 10.
A line across the box at the median, 7.
The whiskers reach out to the smallest, 3, and the biggest, 15.
6 Check
Let's check: the median has 4 numbers below it and 4 above it.
Each half of the plot holds the same count.
So it is right!
Let's look back.
First: put them in order.
Then: find the median.
Then: find Q1 and Q3.
Then: five-number summary.
Then: draw the box plot.
Last: check.