# Box-and-Whisker Plot

See how to make a box-and-whisker plot

(from min to max, excluding outliers).

2 examples and their solutions.

## Box-and-Whisker Plot: from Min to Max

### Example

For the given values, make a box-and-whisker plot.

(Plot type: From minimum to maximum)

1, 2, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

Solution (Plot type: From minimum to maximum)

1, 2, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

1, 2, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

↑

6.5

Q

Q

Q

[2]

↑

6.5

Q

_{1}= 5Q

_{2}= 6.5Q

_{3}= 7 - [1][1]

Find the quartiles of the values.

[2]

Min: 1

Q

Q

Q

Max: 9

Q

_{1}: 5Q

_{2}: 6.5Q

_{3}: 7Max: 9

Close

## Box-and-Whisker Plot: Excluding Outliers

### Example

For the given values, make a box-and-whisker plot.

(Plot type: Excluding outliers)

1, 2, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

Solution (Plot type: Excluding outliers)

1, 2, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

1, 2, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9

↑

6.5

Q

Q

Q

(IQR) = 7 - 5 - [2]

= 2

1.5⋅(IQR) = 1.5⋅2

= 3

[3]

↑

6.5

Q

_{1}= 5Q

_{2}= 6.5Q

_{3}= 7 - [1](IQR) = 7 - 5 - [2]

= 2

1.5⋅(IQR) = 1.5⋅2

= 3

[1]

Find the quartiles of the values.

[2]

IQR: Q

(IQR: Interquartile range)

_{3}- Q_{1}(IQR: Interquartile range)

[3]

Q

Q

Q

Draw the box part.

Draw the 1.5⋅(IQR) regions

at the both sides of the box part.

2 ~ 5, 7 ~ 10

_{1}: 5Q

_{2}: 6.5Q

_{3}: 7Draw the box part.

Draw the 1.5⋅(IQR) regions

at the both sides of the box part.

2 ~ 5, 7 ~ 10

↓

1, 2, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 9 - [4]

↑

6.5

[5]

↑

6.5

[4]

Find the left values that are not in 2 ~ 5.

→ 1: Outlier

Find the right values that are not in 7 ~ 10.

→ None

→ No outliers

→ 1: Outlier

Find the right values that are not in 7 ~ 10.

→ None

→ No outliers

[5]

Left side

Draw the outlier 1.

Draw the left whisker: 2-5.

(2: Min value that is in 2 ~ 5)

Right side

Draw the right whisker: 7-9.

(9: Max value that is in 7 ~ 10)

Draw the outlier 1.

Draw the left whisker: 2-5.

(2: Min value that is in 2 ~ 5)

Right side

Draw the right whisker: 7-9.

(9: Max value that is in 7 ~ 10)

Close