Year 9 Interactive Maths - Second Edition

## Boxplots

A boxplot is a device used to represent the range, median, quartiles and interquartile range of a set of data values.

### Constructing a Boxplot

To construct a boxplot:

(i)   Draw a box to represent the middle 50% of the observations of the data set.
(ii)  Show the median by drawing a vertical line within the box.
(iii)  Draw the lines (called whiskers) from the lower and upper ends of the box to the minimum and maximum values of the data set respectively, as shown in the following diagram.

###### Note:
• X is the set of data values.
• Min X is the minimum value in the data set.
• Max X is the maximum value in the data set.

#### Example 9

Draw a boxplot for the following data set of scores:

76     79     76     74     75     71     85     82     82     79     81

##### Solution:

Arrange the score values in ascending order of magnitude:

71     74     75     76     76     79     79     81     82     82     85

There are 11 values in the data set.

So, the middle half of the scores of the data set lie within a range of 7 units, as shown in the boxplot.