Step by step
The question
Question: draw a box plot of 20, 30, 25, 35, 40, 45, 50 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: 20, 25, 28, 30, 35, 40, 45 and 50.
2 Find the median
8 numbers: two in the middle, 30 and 35.
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.
30 plus 35 is 65.
Divided by 2 is 32.5.
3 Find Q1 and Q3
The lower half has two in the middle: 25 and 28.
Q1 is halfway between them: we add them and divide by 2.
25 plus 28 is 53.
Divided by 2 is 26.5.
The upper half has two in the middle: 40 and 45.
Q3 is halfway between them: we add them and divide by 2.
40 plus 45 is 85.
Divided by 2 is 42.5.
4 Five-number summary
The five-number summary: the smallest 20, Q1 26.5, the median 32.5, Q3 42.5, and the biggest 50.
5 Draw the box plot
A number line from 20 to 50, counting in 5s.
The box goes from Q1, 26.5, to Q3, 42.5.
A line across the box at the median, 32.5.
The whiskers reach out to the smallest, 20, and the biggest, 50.
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.