Step by step
The question
Question: draw a box plot of 105, 98, 112, 120, 95, 108, 115, 101 and 110.
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: 95, 98, 101, 105, 108, 110, 112, 115 and 120.
2 Find the median
9 numbers: 4 on each side of the middle one.
The median is 108.
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: 98 and 101.
Q1 is halfway between them: we add them and divide by 2.
98 plus 101 is 199.
Divided by 2 is 99.5.
The upper half has two in the middle: 112 and 115.
Q3 is halfway between them: we add them and divide by 2.
112 plus 115 is 227.
Divided by 2 is 113.5.
4 Five-number summary
The five-number summary: the smallest 95, Q1 99.5, the median 108, Q3 113.5, and the biggest 120.
5 Draw the box plot
A number line from 95 to 120, counting in 5s.
The box goes from Q1, 99.5, to Q3, 113.5.
A line across the box at the median, 108.
The whiskers reach out to the smallest, 95, and the biggest, 120.
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.