Chapter 13.2, Problem 59E

To determine

To find: If the statement “some quantitative data sets do not have medians” is true or false.

Answer to Problem 59E

The given statement is false based on the explanation given below.

Explanation of Solution

Any quantitative set consists of numerical data which can be either grouped or ungrouped.

For grouped data, the formula for computing the median is given by,

  $M=L+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$

where, L is the lower limit of the median class, n is the sum of all the frequencies, cf is the cumulative frequency of the class before the median class, f is the frequency of the median class and h is the class width.

For ungrouped data, the set is arranged either in ascending or descending order. The value of the median is then determined using the following formula:

  $M=\{\begin{array}{c}\left(\frac{n+1}{2}\right)th\text{ observation , }n\text{ is odd}\\ \frac{\left[\frac{n}{2}th+\left(\frac{n}{2}+1\right)th\right]\text{ observation}}{2}\text{ , }n\text{ is even }\end{array}$

Since in both the cases a median can easily be determined, the given statement is false.