Step by step
The question
Question: draw a box plot of 15, 22, 18, 30, 25, 20, 27, 17, 35, 23, 19 and 28.
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: 15, 17, 18, 19, 20, 22, 23, 25, 27, 28, 30 and 35.
2 Find the median
12 numbers: two in the middle, 22 and 23.
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.
22 plus 23 is 45.
Divided by 2 is 22.5.
3 Find Q1 and Q3
The lower half has two in the middle: 18 and 19.
Q1 is halfway between them: we add them and divide by 2.
18 plus 19 is 37.
Divided by 2 is 18.5.
The upper half has two in the middle: 27 and 28.
Q3 is halfway between them: we add them and divide by 2.
27 plus 28 is 55.
Divided by 2 is 27.5.
4 Five-number summary
The five-number summary: the smallest 15, Q1 18.5, the median 22.5, Q3 27.5, and the biggest 35.
5 Draw the box plot
A number line from 14 to 36, counting in 2s.
The box goes from Q1, 18.5, to Q3, 27.5.
A line across the box at the median, 22.5.
The whiskers reach out to the smallest, 15, and the biggest, 35.
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.