To estimate the median from the provided histogram data, we need to first understand the cumulative frequencies.
The frequency of each category (number of instruments) is represented in the following way:
- 1 instrument: 6
- 2 instruments: 4
- 3 instruments: 1
- 4 instruments: 1
- 5 instruments: 1
Next, we can create a cumulative frequency distribution:
- Cumulative frequency for 1 instrument: 6
- Cumulative frequency for 2 instruments: 6 + 4 = 10
- Cumulative frequency for 3 instruments: 10 + 1 = 11
- Cumulative frequency for 4 instruments: 11 + 1 = 12
- Cumulative frequency for 5 instruments: 12 + 1 = 13
Now, we have a total of 13 data points (sum of frequencies from 1 to 5 instruments).
To find the median, we need to identify the middle value(s). Since there are 13 data points (an odd number), the median will be the value of the 7th data point when arranged in order.
Now, we look at the cumulative frequencies:
- The 1st to the 6th data points correspond to 1 instrument.
- The 7th, 8th, and 9th data points correspond to 2 instruments.
Thus, the 7th data point (and therefore the median) lies in the range of 2 instruments.
Therefore, the median of the data set is 2.