Step by step
The question
Question: draw a box plot of 81, 75, 92, 68, 88, 79, 95, 84, 72 and 90.
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: 68, 72, 75, 79, 81, 84, 88, 90, 92 and 95.
2 Find the median
10 numbers: two in the middle, 81 and 84.
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.
81 plus 84 is 165.
Divided by 2 is 82.5.
3 Find Q1 and Q3
Q1 is the middle of the lower half: 75.
Q3 is the middle of the upper half: 90.
4 Five-number summary
The five-number summary: the smallest 68, Q1 75, the median 82.5, Q3 90, and the biggest 95.
5 Draw the box plot
A number line from 65 to 95, counting in 5s.
The box goes from Q1, 75, to Q3, 90.
A line across the box at the median, 82.5.
The whiskers reach out to the smallest, 68, and the biggest, 95.
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.