To find the median number of musical instruments played, follow these detailed steps:
1. List and Frequency Data:
- Number of instruments: 0, 1, 2, 3
- Frequency: 4, 2, 3, 2
2. Calculate Total Number of Data Points:
We sum the frequencies to find the total number of responses:
[tex]\[
4 + 2 + 3 + 2 = 11
\][/tex]
Therefore, there are 11 total responses.
3. Create the Dataset:
Expand the frequency table into a full list of data points:
- 0 musical instruments: 4 responses → [0, 0, 0, 0]
- 1 musical instrument: 2 responses → [1, 1]
- 2 musical instruments: 3 responses → [2, 2, 2]
- 3 musical instruments: 2 responses → [3, 3]
Combining all these pieces, we obtain:
[tex]\[
[0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3]
\][/tex]
4. Sort the Dataset:
The dataset is already sorted ascendingly from the creation step:
[tex]\[
[0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3]
\][/tex]
5. Determine the Median:
Since the total number of data points (11) is odd:
- The median is the middle value in the sorted list.
- The index of the median in an 11-element list is [tex]\(\frac{11 + 1}{2} = 6\)[/tex].
Counting to the 6th element in the list:
[tex]\[
[0, 0, 0, 0, 1, \mathbf{1}, 2, 2, 2, 3, 3]
\][/tex]
Therefore, the median number of musical instruments played is:
[tex]\[
\boxed{1}
\][/tex]
