Step by step
The question
Question: draw a box plot of 55, 61, 48, 70, 66, 52, 59, 63 and 74.
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: 48, 52, 55, 59, 61, 63, 66, 70 and 74.
2 Find the median
9 numbers: 4 on each side of the middle one.
The median is 61.
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: 52 and 55.
Q1 is halfway between them: we add them and divide by 2.
52 plus 55 is 107.
Divided by 2 is 53.5.
The upper half has two in the middle: 66 and 70.
Q3 is halfway between them: we add them and divide by 2.
66 plus 70 is 136.
Divided by 2 is 68.
4 Five-number summary
The five-number summary: the smallest 48, Q1 53.5, the median 61, Q3 68, and the biggest 74.
5 Draw the box plot
A number line from 45 to 75, counting in 5s.
The box goes from Q1, 53.5, to Q3, 68.
A line across the box at the median, 61.
The whiskers reach out to the smallest, 48, and the biggest, 74.
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.