To determine which measure of center Jesse should use to describe the prices of the 5 guitars given as [tex]$85, $[/tex]90, [tex]$88, $[/tex]82, and $86, let's explore both the mean and the median:
1. Calculating the Mean:
The mean is the sum of all data points divided by the number of data points.
[tex]\[
\text{Mean} = \frac{85 + 90 + 88 + 82 + 86}{5} = \frac{431}{5} = 86.2
\][/tex]
2. Calculating the Median:
The median is the middle value when the numbers are arranged in ascending order. Let's first arrange the prices:
[tex]\[
82, 85, 86, 88, 90
\][/tex]
Since there are 5 numbers, the median will be the third number in this ordered list:
[tex]\[
\text{Median} = 86
\][/tex]
Comparing the mean and the median:
- The mean of the prices is 86.2.
- The median of the prices is 86.
Because the data set does not contain any extreme values (outliers), both the mean and the median are very close to each other. This indicates that either measure of center would be an appropriate choice for describing the prices of these guitars. Therefore, Jesse can use either the mean or the median, as they provide similar information in this case.
The correct answer is:
A. Either the mean or the median. The values are about the same.
