Question

Which data set could be represented by the box plot shown below?

Answer 1

Answer:

Any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.

Step-by-step explanation:

Interpreting Box Plots

A box plot is used to present the 5-Number summary of a set of data.

The 5-Number summary consists of the following in their order of appearance on the box plot.

• Minimum Value
• First Quartile, $Q_1$
• Median, $Q_2$
• Third Quartile, $Q_3$
• Maximum Value

In the box plot, the following rules applies

• The whisker starts from the minimum value and ends at the first quartile.

• The box starts at the first quartile and ends at the third quartile. There is a vertical line inside the box which shows the median.
• The end whisker starts at the third quartile and ends at the maximum value.

Using these, we interpret the given box plot

A left whisker extends from 1 to 6.

• Minimum Value=1
• First Quartile =6

The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12.

• Median=12
• Thrid Quartile=16

The right whisker extends from 16 to 19.

• Maximum Value =19

Therefore any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.