Question

What is the mean minimum wage of the 20 states in the table above? (Ignore the work)

Answer 1

B) $7.70

Explanation:

Given frequency table:

`\begin{array}c\cline{1-2}\vphantom{\frac12}\textsf{Minimum Wage $(x)$}&\textsf{Number of States $(f)$}\\\cline{1-2}\vphantom{\frac12}\$7.25&16\\\cline{1-2}\vphantom{\frac12}\$8.25&3\\\cline{1-2}\vphantom{\frac12}\$13.25&1\\\cline{1-2}\end{array}`

In the given frequency table, the category of data (x) is the minimum wage, and the frequency (f) is the number of states with that wage.

To determine the mean of the data values in a frequency table, multiply each x-value by its corresponding frequency, sum these products, and then divide by the total frequency.

Therefore, the formula for the mean can be expressed as:

`\textsf{Mean}=(\displaystyle\sum xf)/(\displaystyle\sum f)`

Hence, the mean minimum wage can be calculated as follows:

`\textsf{Mean}=(\$7.25 * 16+\$8.25 * 3+\$13.25 * 1)/(16+3+1)`

`\textsf{Mean}=(\$116.00+\$24.75+\$13.25)/(20)`

`\textsf{Mean}=(\$154)/(20)`

`\textsf{Mean}=\$7.70`

So, the mean minimum wage for the 20 states is $7.70.

Answer 2

B. $ 7.70

Explanation:

Given:

Minimum wages : $ 7.25 , $8.25 and $13.25

Number of states : 16, 3 and 1

To find:

Mean of 20 states.

Solution:

The mean of a set of numbers is the average of those numbers. It is calculated by adding all of the numbers in the set and then dividing by the number of numbers in the set.

In order to calculate the mean, we can use the following formula:

`\sf Mean = \frac{\textsf{Sum of all values}}{\textsf{Number of values}}`

Substituting value:

`\sf Mean = ( \$7.25 \cdot 16 + \$8.25 \cdot 3 + \$13.25 \cdot 1 )/(16+3+1)`

`\sf Mean = (\$116 + \$ 24.75 + \$13.25)/(20)`

`\sf Mean = (\$154)/(20)`

`\sf Mean = \$ 7.70`

Therefore, the mean of the minimum wages of 20 states is B. $7.70.