To find the five-number summary for the given data set of movie lengths, follow these steps:
1. Arrange the data in ascending order.
2. Identify the minimum value.
3. Find the first quartile (Q1), which is the median of the lower half of the data.
4. Find the median (Q2) of the entire data set.
5. Find the third quartile (Q3), which is the median of the upper half of the data.
6. Identify the maximum value.
Here's the data set provided:
[tex]\[ \{8, 1, 3, 9, 0, 3, 7, 10, 4, 4, 7, 9, 11, 1, 3, 5, 12, 5, 9, 9, 13, 2, 6\} \][/tex]
Step-by-step breakdown:
1. Arrange the data in ascending order:
[tex]\[ \{0, 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 9, 9, 10, 11, 12, 13\} \][/tex]
2. Identify the minimum value:
[tex]\[ \text{Minimum} = 0 \][/tex]
3. Find the first quartile (Q1):
[tex]\[ Q1 = 3.0 \][/tex]
4. Find the median (Q2):
[tex]\[ \text{Median} = 6.0 \][/tex]
5. Find the third quartile (Q3):
[tex]\[ Q3 = 9.0 \][/tex]
6. Identify the maximum value:
[tex]\[ \text{Maximum} = 13 \][/tex]
Therefore, the five-number summary for the data is:
- The minimum of the data is [tex]\( \boxed{0} \)[/tex]
- The first quartile is [tex]\( \boxed{3.0} \)[/tex]
- The median of the data is [tex]\( \boxed{6.0} \)[/tex]
- The third quartile is [tex]\( \boxed{9.0} \)[/tex]
- The maximum of the data is [tex]\( \boxed{13} \)[/tex]
