Step by step
The question
Question: draw a box plot of 62, 58, 71, 65, 54, 68, 75 and 60.
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: 54, 58, 60, 62, 65, 68, 71 and 75.
2 Find the median
8 numbers: two in the middle, 62 and 65.
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.
62 plus 65 is 127.
Divided by 2 is 63.5.
3 Find Q1 and Q3
The lower half has two in the middle: 58 and 60.
Q1 is halfway between them: we add them and divide by 2.
58 plus 60 is 118.
Divided by 2 is 59.
The upper half has two in the middle: 68 and 71.
Q3 is halfway between them: we add them and divide by 2.
68 plus 71 is 139.
Divided by 2 is 69.5.
4 Five-number summary
The five-number summary: the smallest 54, Q1 59, the median 63.5, Q3 69.5, and the biggest 75.
5 Draw the box plot
A number line from 54 to 76, counting in 2s.
The box goes from Q1, 59, to Q3, 69.5.
A line across the box at the median, 63.5.
The whiskers reach out to the smallest, 54, and the biggest, 75.
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.