Question

calculating measures of center
raelyns weekly wages
raelyn is working as a lifeguard at the local pool during the summer. her weekly wages are $424, $562, $330, and $549.
what is the mean of raelyns wages?
what is the median of raelyns wages?
what is the mode of raelyns wages?

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 6$, and the data points are $x_1=216,x_2 = 330,x_3=330,x_4 = 424,x_5=549,x_6=562$.

Step2: Calculate the sum

$\sum_{i = 1}^{6}x_{i}=216 + 330+330+424+549+562=2411$.

Step3: Calculate the mean

$\bar{x}=\frac{2411}{6}\approx401.83$.

Step4: Recall median formula

For $n = 6$ (an even number of data - points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. First, order the data: $216,330,330,424,549,562$. $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$. The 3rd and 4th ordered data - points are $330$ and $424$. The median $M=\frac{330 + 424}{2}=\frac{754}{2}=377$.

Step5: Recall mode definition

The mode is the data - point that appears most frequently. In the set $\{216,330,330,424,549,562\}$, the number $330$ appears twice and the other numbers appear once, so the mode is $330$.

Answer:

Mean: $401.83$
Median: $377$
Mode: $330$