Step by step
The question
Question: draw a box plot of 1, 1, 2, 3, 3, 4, 5, 6, 6, 8, 9 and 12.
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: 1, 1, 2, 3, 3, 4, 5, 6, 6, 8, 9 and 12.
2 Find the median
12 numbers: two in the middle, 4 and 5.
The median goes between them.
It cuts the list in two halves, 6 numbers each.
The median is halfway between them: we add them and divide by 2.
4 plus 5 is 9.
Divided by 2 is 4.5.
3 Find Q1 and Q3
The lower half has two in the middle: 2 and 3.
Q1 is halfway between them: we add them and divide by 2.
2 plus 3 is 5.
Divided by 2 is 2.5.
The upper half has two in the middle: 6 and 8.
Q3 is halfway between them: we add them and divide by 2.
6 plus 8 is 14.
Divided by 2 is 7.
4 Five-number summary
The five-number summary: the smallest 1, Q1 2.5, the median 4.5, Q3 7, and the biggest 12.
5 Draw the box plot
A number line from 1 to 12.
The box goes from Q1, 2.5, to Q3, 7.
A line across the box at the median, 4.5.
The whiskers reach out to the smallest, 1, and the biggest, 12.
6 Check
Let's check: the median has 6 numbers below it and 6 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.