Box-and-Whisker Plot

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

The following data show quiz scores for 14 students: 7, 5, 4, 7, 8, 5, 9, 1, 4, 7, 7, 8, 5, 6. Draw a box-and-whisker plot for the data. (Plot type: from min. to max.)

Find Q2 (2nd quartile):
the median.
Q2 = 6.5.

Find Q1 (1st quartile):
the median of the lower half.
Q1 = 5

Find Q3 (3rd quartile):
the median of the upper half.
Q3 = 7

Draw five dots:
(min) = 1, Q1 = 5, Q2 = 6.5, Q3 = 7, (max) = 9.

Draw a box that passes through Q1 and Q3.

Draw a vertical line that passes through Q2.

Draw the whiskers by connecting
(min)-Q1 and Q3-(max).

Example 2: Excluding Outliers

The following data show quiz scores for 14 students: 7, 5, 4, 7, 8, 5, 9, 1, 4, 7, 7, 8, 5, 6. Draw a box-and-whisker plot for the data. (Plot type: excluding outliers)

Find Q2 (2nd quartile):
the median.
Q2 = 6.5.

Find Q1 (1st quartile):
the median of the lower half.
Q1 = 5

Find Q3 (3rd quartile):
the median of the upper half.
Q3 = 7

Find the IQR (Inter-Quartile Range):
(IQR) = Q3 - Q1 = 2

Find the 1.5(IQR):
1.5(IQR) = 3.

Find the 1.5(IQR) range.

Q1 - 1.5(IQR) = 2(start point) = 2
Q3 + 1.5(IQR) = 10(end point) = 10

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

Draw five dots:
(min) = 1, Q1 = 5, Q2 = 6.5, Q3 = 7, (max) = 9.

Draw a box that passes through Q1 and Q3.

Draw a vertical line that passes through Q2.

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)-Q1 and Q3-(max).

Leave the (min).
It's the outlier. (red)