Chapter 13.1, Problem 4GP

To determine

To find: the best measure of data to describe the performance.

Answer to Problem 4GP

The best performance will be median, $11.95\text{sec}$

Explanation of Solution

Given information:

The given data is as follows $11.6,11.8,12.7,12.6,11.9,12.0$

Calculation:

Find the median

  $\begin{array}{l}\text{mean=}\frac{\text{sum of data}}{\text{ number of samples}}\\ =\frac{11.6+11.8+12.7+12.6+11.9+12.0}{6}\\ =\frac{72.6}{6}\\ =12.1\end{array}$

Find the mean

Write the data in ascending order as follows

  $11.6,11.8,11.9,12.0,12.6,12.7$

Median is the mean value of the middle numbers.

  $\begin{array}{l}\text{median}=\frac{11.9+12.0}{2}\\ =\frac{23.9}{2}\\ =11.95\end{array}$

Find the mode

There are no repeated numbers in the data, so we cannot find the mode of the data.

By observing the values of mean and median, the median has the smallest value.

Hence,

The best performance will be median, $11.95\text{sec}$