Question

an insurance company crashed four cars of the same model at 5 miles per hour. the costs of repair for each of the four crashes were $441, $404, $457, and $237. compute the mean, median, and mode cost of repair.
compute the mean cost of repair. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the mean cost of repair is $ (round to the nearest cent as needed.)
b. the mean does not exist.
compute the median cost of repair. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the median cost of repair is $ (round to the nearest cent as needed.)
b. the median does not exist.
compute the mode cost of repair. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the mode cost of repair is $ (round to the nearest cent as needed.)
b. the mode does not exist.

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a set of data $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 4$, $x_1=441$, $x_2 = 404$, $x_3=457$, $x_4=237$.
$\sum_{i=1}^{4}x_i=441 + 404+457+237=1539$.
$\bar{x}=\frac{1539}{4}=384.75$.

Step2: Calculate the median

First, order the data: $237,404,441,457$.
Since $n = 4$ (an even number), the median $M$ is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th values.
The $\frac{n}{2}=2$-th value is $404$ and the $(\frac{n}{2}+1) = 3$-th value is $441$.
$M=\frac{404 + 441}{2}=\frac{845}{2}=422.5$.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data set.
In the set $\{237,404,441,457\}$, each value appears exactly once.

Answer:

• Mean: A. The mean cost of repair is $\$384.75$.
• Median: A. The median cost of repair is $\$422.5$.
• Mode: B. The mode does not exist.