Chapter 15.1, Problem 6OE

To determine

Find the median.

Answer to Problem 6OE

  $32$ .

Explanation of Solution

Given information:

Use the stem-and-leaf plot below

  $\begin{array}{cccccc}1& 2,& 2,& 7,& 8& \\ 2& 3,& 4,& 5,& 5,& 9\\ 3& 2,& 2,& 2,& 6,& 8\\ 4& 0,& 0,& 0,& 0,& 6\\ 5& 0& & & & \end{array}$

Calculation:

Let us consider the stem-and-leaf plot,

  $\begin{array}{cccccc}1& 2,& 2,& 7,& 8& \\ 2& 3,& 4,& 5,& 5,& 9\\ 3& 2,& 2,& 2,& 6,& 8\\ 4& 0,& 0,& 0,& 0,& 6\\ 5& 0& & & & \end{array}$

There are $20$ observations, which is even,

so, the mean of ${\left(\frac{n}{2}\right)}^{th}and{\left(\frac{n}{2}+1\right)}^{th}$ observation is the median.

Here, we have,

  $\begin{array}{l}{\left(\frac{n}{2}\right)}^{th}={\left(\frac{20}{2}\right)}^{th}={10}^{{}^{th}}term=32\\ {\left(\frac{n}{2}+1\right)}^{th}={\left(\frac{20}{2}+1\right)}^{th}={11}^{{}^{th}}term=32\\ so,\\ Median=\frac{32+32}{2}=\frac{64}{2}=32\end{array}$

Hence, the median is $32$ .