Question

the table shows information about how many musical instruments some students play.

what is the median number of musical instruments played?

Explanation:

Calculate total frequency

Using the Frequency Table knowledge point, we sum the frequencies to find the total number of students \(N\):

$$ N = 3 + 2 + 2 + 4 = 11 $$

Find the median position

Since the total number of students \(N = 11\) is odd, the median is the value at the following position:

$$ \text{Position} = \frac{N + 1}{2} = \frac{11 + 1}{2} = 6\text{th position} $$

Determine the median value

We find the 6th value by calculating the cumulative frequencies:

• Cumulative frequency for 0 instruments: \(3\) (covers positions 1 to 3)
• Cumulative frequency for 1 instrument: \(3 + 2 = 5\) (covers positions 4 to 5)
• Cumulative frequency for 2 instruments: \(5 + 2 = 7\) (covers positions 6 to 7)

Since the 6th position falls within the group of students who play 2 instruments, the median is 2.

Answer:

2