# Box-and-Whisker Plot

How to draw a box-and-whisker plot based on the given data: example and its solution. (Plot type: from minimum to maximum, excluding outliers)

## Example 1: from Minimum to Maximum

Find *Q*_{2} (2nd quartile):

the median.*Q*_{2} = 6.5.

Find *Q*_{1} (1st quartile):

the median of the lower half.*Q*_{1} = 5

Find *Q*_{3} (3rd quartile):

the median of the upper half.*Q*_{3} = 7

Draw five dots:

(min) = 1, *Q*_{1} = 5, *Q*_{2} = 6.5, *Q*_{3} = 7, (max) = 9.

Draw a box that passes through *Q*_{1} and *Q*_{3}.

Draw a vertical line that passes through *Q*_{2}.

Draw the whiskers by connecting

(min)-*Q*_{1} and *Q*_{3}-(max).

## Example 2: Excluding Outliers

Find *Q*_{2} (2nd quartile):

the median.*Q*_{2} = 6.5.

Find *Q*_{1} (1st quartile):

the median of the lower half.*Q*_{1} = 5

Find *Q*_{3} (3rd quartile):

the median of the upper half.*Q*_{3} = 7

Find the IQR (Inter-Quartile Range):

(IQR) = *Q*_{3} - *Q*_{1} = 2

Find the 1.5(IQR):

1.5(IQR) = 3.

Find the 1.5(IQR) range.*Q*_{1} - 1.5(IQR) = 2→(start point) = 2*Q*_{3} + 1.5(IQR) = 10→(end point) = 10

1.5(IQR) range: 2 ~ 5, 7 ~ 10

Draw five dots:

(min) = 1, *Q*_{1} = 5, *Q*_{2} = 6.5, *Q*_{3} = 7, (max) = 9.

Draw a box that passes through *Q*_{1} and *Q*_{3}.

Draw a vertical line that passes through *Q*_{2}.

Before drawing the whiskers,

see if (min) and (max) are in the 1.5(IQR) range:

2 ~ 5, 7 ~ 10.

(min) = 1 is out of the range.

So draw the (start point): 2.

(max) = 9 is in the range.

Then you don't need to draw (end point): 10.

Draw the whiskers by connecting

(start point)-*Q*_{1} and *Q*_{3}-(max).

Leave the (min).

It's the outlier. (red)