Chapter 14.2, Problem 18E

To determine

To find: The mean median and mode of the data represented by each stem-and-leaf plot.

Answer to Problem 18E

The mean, median and mode are given below.

Explanation of Solution

Given:

The set of data is as:

  $\left\{5.2,5.4,5.6,6.0,6.1,6.7,6.8,6.9,7.1,7.6,8.0,8.2,8.6,9.1\right\}$

Calculation:

The mean median and mode are calculated as:

  $\begin{array}{c}\overline{x}=\frac{\text{Sum of all values}}{\text{Total number of value}}\\ \overline{x}=\frac{5.2+5.4+5.6+6.0+6.1+6.7+6.8+6.9+7.1+7.6+8.0+8.2+8.6+9.1}{14}\\ \approx 6.95\\ \text{Median}=\frac{1}{2}\left(\left(\frac{N}{2}\right)\text{th term}+\left(\frac{N}{2}+1\right)\text{th term}\right)\end{array}$

Further simplified as:

  $\begin{array}{c}\text{Median}=\left(\frac{\text{7th term}+8\text{th term}}{2}\right)\\ =\frac{6.8+6.9}{2}\\ =6.85\end{array}$

The mode is the number that appears more frequently of that any other in the set.

In the given data there does not exist any frequent number. So there is no mode.

Therefore the mean, median and mode are given above.