Step by step
The question
Question: draw a box plot of 3, 7, 8, 5, 12, 14, 21, 13 and 18.
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, 5, 7, 8, 12, 13, 14, 18 and 21.
2 Find the median
9 numbers: 4 on each side of the middle one.
The median is 12.
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: 5 and 7.
Q1 is halfway between them: we add them and divide by 2.
5 plus 7 is 12.
Divided by 2 is 6.
The upper half has two in the middle: 14 and 18.
Q3 is halfway between them: we add them and divide by 2.
14 plus 18 is 32.
Divided by 2 is 16.
4 Five-number summary
The five-number summary: the smallest 3, Q1 6, the median 12, Q3 16, and the biggest 21.
5 Draw the box plot
A number line from 2 to 22, counting in 2s.
The box goes from Q1, 6, to Q3, 16.
A line across the box at the median, 12.
The whiskers reach out to the smallest, 3, and the biggest, 21.
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.