## Related questions with answers

The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.

Compute the range and interquartile range.

Solutions

VerifiedTo calculate the range and interquartile range we need to arrange the data in ascending order as follows:

$28 \quad 42\quad45\quad48\quad49\quad50\quad55\quad58\quad60$

First, we will calculate the Range as follows:

$\text { Range }=\text { Largest value }-\text { Smallest value } =60-28=32$

The range is difference between maximum and minimum values in the data array:

$\begin{gather*} Range = 60 - 28 = 32 \end{gather*}$

Interquartile range is difference between third and first quartile value, first find first and third quartile and then compute the IQR.

$\begin{gather*} Q_1 = 0.25 \cdot 9 = 2.25 \approx 3 \implies Q_1 = 45\\ Q_3 = 0.75 \cdot 9 = 6.75 \approx 7 \implies Q_3 = 55\\ IQR = Q_3 - Q_1 = 55 - 45 =10\\ \end{gather*}$

In this exercise, we calculate the range and interquartile range of the given data.

*How can the range be derived?*

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