Step by step
The question
Question: draw a box plot of 15, 22, 9, 30, 18, 25 and 12.
A box plot shows how the numbers spread out.
The box holds the middle half.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Put them in order
First we put them in order, smallest first: 9, 12, 15, 18, 22, 25 and 30.
2 Find the median
The median is the middle number.
7 numbers: 3 on each side of the middle one.
The median is 18.
3 Find Q1 and Q3
The median cuts the list in two halves, 3 numbers each.
The median itself is in neither half.
Careful!
The median is not counted in the halves.
Each half has 3 numbers.
The quartiles cut the list into four quarters.
Q1 is the middle of the lower half.
Q3 is the middle of the upper half.
Q1 is the middle of the lower half: 12.
Q3 is the middle of the upper half: 25.
4 Five-number summary
The five-number summary: the smallest 9, Q1 12, the median 18, Q3 25, and the biggest 30.
5 Draw the box plot
A number line from 8 to 30, counting in 2s.
The box goes from Q1, 12, to Q3, 25.
A line across the box at the median, 18.
The whiskers reach out to the smallest, 9, and the biggest, 30.
6 Check
Let's check: the median has 3 numbers below it and 3 above it.
Each half of the plot holds the same count.
So it is right!
7 Pick the choice
Our answer is min 9, Q1 12, median 18, Q3 25, max 30.
That is choice C.
8 Why not the others
A is min 9, Q1 13.5, median 18, Q3 23.5, max 30.
Wrong: put the median into both halves: leave it out.
B is min 9, Q1 15, median 18, Q3 22, max 30.
Wrong: Q1 and Q3 are the middles of the halves, not the values next to the median.
D is min 9, Q1 12, median 18.71, Q3 25, max 30.
Wrong: 18.71 is the mean, not the median.
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.
Then: check.
Then: pick the choice.
Last: why not the others.