Step by step
The question
Question: draw a box plot of 4, 9, 6, 2, 11, 7, 8 and 5.
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: 2, 4, 5, 6, 7, 8, 9 and 11.
2 Find the median
8 numbers: two in the middle, 6 and 7.
The median goes between them.
It cuts the list in two halves, 4 numbers each.
The median is halfway between them: we add them and divide by 2.
6 plus 7 is 13.
Divided by 2 is 6.5.
3 Find Q1 and Q3
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: 8 and 9.
Q3 is halfway between them: we add them and divide by 2.
8 plus 9 is 17.
Divided by 2 is 8.5.
4 Five-number summary
The five-number summary: the smallest 2, Q1 4.5, the median 6.5, Q3 8.5, and the biggest 11.
5 Draw the box plot
A number line from 2 to 11.
The box goes from Q1, 4.5, to Q3, 8.5.
A line across the box at the median, 6.5.
The whiskers reach out to the smallest, 2, and the biggest, 11.
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.