Step by step
The question
Question: draw a box plot of 12, 45, 23, 38, 17, 29, 51, 34, 26, 40 and 19.
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: 12, 17, 19, 23, 26, 29, 34, 38, 40, 45 and 51.
2 Find the median
11 numbers: 5 on each side of the middle one.
The median is 29.
3 Find Q1 and Q3
The median cuts the list in two halves, 5 numbers each.
The median itself is in neither half.
Careful!
The median is not counted in the halves.
Each half has 5 numbers.
Q1 is the middle of the lower half: 19.
Q3 is the middle of the upper half: 40.
4 Five-number summary
The five-number summary: the smallest 12, Q1 19, the median 29, Q3 40, and the biggest 51.
5 Draw the box plot
A number line from 10 to 55, counting in 5s.
The box goes from Q1, 19, to Q3, 40.
A line across the box at the median, 29.
The whiskers reach out to the smallest, 12, and the biggest, 51.
6 Check
Let's check: the median has 5 numbers below it and 5 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.