To determine the median number of musical instruments played using the given frequency table, follow these detailed steps:
1. Construct the Data Set:
- The frequency table tells us how many times each number of instruments appear.
- Number of people playing 0 instruments: 3 times.
- Number of people playing 1 instrument: 2 times.
- Number of people playing 2 instruments: 2 times.
- Number of people playing 3 instruments: 4 times.
Based on this information, we construct the data set:
[tex]\[
\{0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 3\}
\][/tex]
2. Sort the Data Set:
- The data set is already sorted:
[tex]\[
\{0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 3\}
\][/tex]
3. Determine the Median:
- The median is the middle value of a data set when it is ordered from least to greatest.
- First, calculate the number of data points ([tex]\(n\)[/tex]):
[tex]\[
n = 11
\][/tex]
- Since the number of data points is odd ([tex]\(n = 11\)[/tex]), the median is the value at the position:
[tex]\[
\text{Median Position} = \frac{n + 1}{2} = \frac{11 + 1}{2} = 6
\][/tex]
- The value at the 6th position of the sorted data set is 2.
Therefore, the median number of musical instruments played is [tex]\(2\)[/tex].
