Question

michael checked several websites and stores around town for the television he wanted to purchase. he saw eight different prices: $224 $267 $254 $242 $270 $283 $245 $267 what is the mean, median, and mode of this data set? mean = $260.50 median = $283 mode = $256.50 mean = $256.50 median = $260.50 mode = $267 mean = $267 median = $256.50 mode = $283 mean = $260.50 median = $267 mode = $256.50

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 8$ and $x_{i}$ are the data points.
$\sum_{i=1}^{8}x_{i}=224 + 267+254 + 242+270+283+245+267=2052$
$\bar{x}=\frac{2052}{8}=256.5$

Step2: Find the median

First, order the data: $224,242,245,254,267,267,270,283$.
Since $n = 8$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
$x_{4}=254$ and $x_{5}=267$
$M=\frac{254 + 267}{2}=260.5$

Step3: Determine the mode

The mode is the data point that appears most frequently. The number $267$ appears twice, more frequently than other values.

Answer:

Mean = $\$256.50$, Median = $\$260.50$, Mode = $\$267$