Chapter 13, Problem 5MCQ

To determine

To find: The measure of variation for the given set of data

Answer to Problem 5MCQ

Range is $7$

Median is $24$

Lower quartile is $22.5$

Upper quartile is $25.5$

Interquartile range is $3$

Explanation of Solution

Given:

Numbers of students in the homerooms at Morgan Middle School are

  $\text{22,21,24,23,26,23,28,24,25}$

Calculation:

The given data is $\text{22,21,24,23,26,23,28,24,25}$

Arrange this set of the data in numeric order

  $\text{21, 22, 23, 23, 24, 24, 25, 26, 28}$

Hence, the range is given by

  $\begin{array}{c}\text{Range }=\text{ maximum value}-\text{minimum value }\\ =28-21\\ =7\end{array}$

The median is given by $24$

The lower quartile is the median of the left half of the data.

So, lower quartile is given by

  $\begin{array}{c}{Q}_1=\frac{22+23}{2}\\ =\frac{45}{2}\\ =22.5\end{array}$

The upper quartile is the median of the right half of the data.

So, upper quartile is given by

  $\begin{array}{c}{Q}_3=\frac{25+26}{2}\\ =\frac{51}{2}\\ =25.5\end{array}$

Therefore, the interquartile range is given by

  $\begin{array}{c}IQR=Q_3-Q_1\\ =25.5-22.5\\ =3\end{array}$