Question

1. 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 sum of prices

$699 + 599+699+680+590+720+650+800 = 5437$

Step2: Calculate the mean

The number of data - points $n = 8$. The mean $\bar{x}=\frac{5437}{8}=679.625\approx679.63$

Step3: Arrange prices in ascending order

$590,599,650,680,699,699,720,800$

Step4: Calculate the median

Since $n = 8$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values. The $\frac{8}{2}=4$th value is $680$ and the $(\frac{8}{2}+1) = 5$th value is $699$. Median $=\frac{680 + 699}{2}=\frac{1379}{2}=689.5$

Step5: Find the mode

The mode is the value that appears most frequently. Here, $699$ appears twice and other values appear once, so the mode is $699$.

Answer:

A. $\$679.63$
B. $\$689.50$
C. $\$699$