Chapter 13.1, Problem 11PPS

To determine

To find: Which measure of central tendency might Matthew wants to use to describe his test scores.

Answer to Problem 11PPS

Matthew wants to use median to describe his test scores.

Explanation of Solution

Given:

Matthew’s math test scores this semester were $80,76,94,90,88,92,88,96$

Calculation:

The given data is $80,76,94,90,88,92,88,96$

Find mean, medina and mode of this data.

  $\begin{array}{c}\text{mean}=\frac{\text{Sum of observations}}{\text{Number of observtions}}\\ =\frac{80+76+94+90+88+92+88+96}{8}\\ =\frac{704}{8}\\ =88\end{array}$

In order to find the median arrange this data in numeric order

  $76,80,88,88,90,92,94,96$

The number of data is 8 which is even. So median will be the average of 4^th and 5^th data.

So, median is given by

  $\begin{array}{l}\frac{88+90}{2}\\ =\frac{178}{2}\\ =89\end{array}$

Now, in the given set of data, the number 88 occurs twice.

So, the mode is 88.

Among the mean, median and mode, the greatest is median.

Therefore, Matthew wants to use median to describe his test scores.