Question

kate is a professional musician. she wants to make an essential purchase of an upgraded used bass guitar for her work. she found the following prices for the same make and model bass guitar from various sellers: $699, $599, $699, $680, $590, $720, $650, $800. a. what is the mean price? round your answer to the nearest cent. b. what is the median price? c. what is the mode price?

Explanation:

Step1: Calculate the mean

The mean formula is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points.
First, sum the prices: $699+599+699+680+590+720+650+800 = 5437$.
There are $n = 8$ prices.
The mean is $\frac{5437}{8}=679.625\approx\$679.63$.

Step2: Calculate the median

Arrange the prices in ascending order: $590,599,650,680,699,699,720,800$.
Since $n = 8$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points.
The $\frac{n}{2}=4$th value is $680$ and the $(\frac{n}{2}+1) = 5$th value is $699$.
The median is $\frac{680 + 699}{2}=\frac{1379}{2}=\$689.50$.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data - set.
The price $\$699$ appears $2$ times, more frequently than any other price, so the mode is $\$699.00$.

Answer:

a. $\$679.63$
b. $\$689.50$
c. $\$699.00$