Question

the dot - plot represents the distribution of wages earned during a one - week period by 12 college students. what is the mean? $\square$ what is the median? $\square$ weekly wages (dollars)

Explanation:

Step1: Determine the frequency of each value

From the dot - plot:
Value 112 has 1 dot, value 114 has 1 dot, value 116 has 3 dots, value 118 has 2 dots, value 120 has 2 dots, value 124 has 3 dots.

Step2: Calculate the sum of all values

\[

$$\begin{align*} \text{Sum}&=(112\times1)+(114\times1)+(116\times3)+(118\times2)+(120\times2)+(124\times3)\\ &=112 + 114+348+236+240+372\\ &=(112 + 114)+348+(236+240)+372\\ &=226+348 + 476+372\\ &=(226+348)+(476+372)\\ &=574+848\\ &=1422 \end{align*}$$

\]

Step3: Calculate the mean

The number of data points \(n = 12\). The mean \(\bar{x}=\frac{\text{Sum}}{n}=\frac{1422}{12}=118.5\)

Step4: Arrange the data in ascending order

The data set in ascending order: \(112,114,116,116,116,118,118,120,120,124,124,124\)

Step5: Calculate the median

Since \(n = 12\) (an even - numbered data set), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered data values. \(\frac{n}{2}=6\) and \(\frac{n}{2}+1 = 7\). The 6th value is 118 and the 7th value is 118. So the median \(\text{Median}=\frac{118 + 118}{2}=118\)

Answer:

Mean: \(118.5\)
Median: \(118\)