To determine which intervals are appropriate for creating a histogram of the given movie ticket sales data, let's examine each option step-by-step.
The data provided is:
[tex]\[8, 15, 47, 12, 52, 27, 29, 32, 83, 77\][/tex]
1. Intervals: 0-14, 15-29, 30-44, 45-59, 60-75
- We would need to check if all the ticket sales fit into these intervals.
- Minimum value = 8 (falls into 0-14)
- Maximum value = 83 (does not fall into any range provided; the highest range is 60-75)
- Therefore, these intervals are not appropriate, as they do not cover the entire range of data.
2. Intervals: 0-25, 25-50, 50-75, 75-100
- Again, check if all ticket sales fit within these intervals.
- Minimum value = 8 (falls into 0-25)
- Maximum value = 83 (falls into 75-100)
- All other values (15, 47, 12, 52, 27, 29, 32, 77) also fit into one of these intervals.
- Therefore, these intervals are appropriate, as they cover all the ticket sales data.
3. Intervals: 0-19, 20-39, 40-59, 60-79, 80-99
- Check if all ticket sales fit within these intervals.
- Minimum value = 8 (falls into 0-19)
- Maximum value = 83 (falls into 80-99)
- All other values (15, 47, 12, 52, 27, 29, 32, 77) also fit into one of these intervals.
- Therefore, these intervals are appropriate, as they cover all the ticket sales data.
4. Intervals: 0-20, 20-35, 35-50, 55-70, 75-90
- Check if all ticket sales fit within these intervals.
- Minimum value = 8 (falls into 0-20)
- Maximum value = 83 (falls into 75-90)
- Value 47 (does not fit into any of the intervals due to the gap between 50 and 55)
- Therefore, these intervals are not appropriate, as they have gaps that leave some data out.
Upon reviewing all the options, the appropriate intervals for creating the histogram of the provided ticket sales data are:
[tex]\[ 0-25, 25-50, 50-75, 75-100 \][/tex]
[tex]\[ 0-19, 20-39, 40-59, 60-79, 80-99 \][/tex]
Thus, the correct answers are:
[tex]\[ \boxed{2, 3} \][/tex]
