Step by step
The question
Question: draw a box plot of 21, 35, 28, 40, 33, 26, 38, 30, 45 and 24.
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: 21, 24, 26, 28, 30, 33, 35, 38, 40 and 45.
2 Find the median
10 numbers: two in the middle, 30 and 33.
The median goes between them.
It cuts the list in two halves, 5 numbers each.
The median is halfway between them: we add them and divide by 2.
30 plus 33 is 63.
Divided by 2 is 31.5.
3 Find Q1 and Q3
Q1 is the middle of the lower half: 26.
Q3 is the middle of the upper half: 38.
4 Five-number summary
The five-number summary: the smallest 21, Q1 26, the median 31.5, Q3 38, and the biggest 45.
5 Draw the box plot
A number line from 20 to 46, counting in 2s.
The box goes from Q1, 26, to Q3, 38.
A line across the box at the median, 31.5.
The whiskers reach out to the smallest, 21, and the biggest, 45.
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.