A set of Pollutant Standards Index (PSI) taken from different parts of Singapore is as follows. 28 30 48 19 70 50 32 72 Represent the data using a box-and-whisker plot.

1. Arrange the data in ascending order.

Given data:

$28,\ 30,\ 48,\ 19,\ 70,\ 50,\ 32,\ 72$

In ascending order:

$19,\ 28,\ 30,\ 32,\ 48,\ 50,\ 70,\ 72$

2. Find the five-number summary needed for the box-and-whisker plot.

There are $8$ values.

Minimum $=19$, maximum $=72$.

Median:

$\frac{32+48}{2}=40$

Lower quartile:

$Q_1=\frac{28+30}{2}=29$

Upper quartile:

$Q_3=\frac{50+70}{2}=60$

3. Represent the five-number summary as a box-and-whisker plot.

Use a suitable horizontal scale for PSI.

Plot and label:

• minimum $19$
• lower quartile $29$
• median $40$
• upper quartile $60$
• maximum $72$

Draw the box from $29$ to $60$, draw a vertical line at $40$, and draw whiskers to $19$ and $72$.