Q8. - Algebra 1

Question

Which measure of central tendency best represents the data? Justify your answer. Then find the measure.

VOTING The polling place kept a list of all the ages of the people who voted:

$\mathbf{21}\mathbf{,}\mathbf{25}\mathbf{,}\mathbf{32}\mathbf{,}\mathbf{41}\mathbf{,}\mathbf{32}\mathbf{,}\mathbf{20}\mathbf{,}\mathbf{65}\mathbf{,}\mathbf{33}\mathbf{,}\mathbf{30}\mathbf{,}\mathbf{72}$

Step-by-Step Solution

Answer

The measure of central tendency best represents the data is mean. The mean value of given data is $\mathbf{37}\mathbf{.}\mathbf{1}$.

Step 1. List the values from least to greatest.

The list of given values from the least to greatest is

$20,21,25,30,32,32,33,41,65,72$

Step 2. Measure of central tendency.

Data represents the age of people who voted so, the mean value represents the average age of the people who voted.

Therefore, mean represents the data.

Step 3. Find the mean.

To find the mean of the given data, add all data and divide it by amount of data.

$\begin{array}{l}\text{mean}=\frac{20+21+25+30+32+33+41+65+72}{10}\\ =\frac{371}{10}\\ =37.1\end{array}$

The mean value of given data is $37.1$.