Certainly! Let's determine the mode for each of the given datasets. The mode is the value that appears the most frequently in a dataset.
### Dataset 1: [tex]\(2, 3, 5, 6, 8, 9, 9\)[/tex]
- Frequency Count:
- 2 occurs 1 time
- 3 occurs 1 time
- 5 occurs 1 time
- 6 occurs 1 time
- 8 occurs 1 time
- 9 occurs 2 times
Since 9 appears the most frequently (2 times), the mode for this dataset is:
[tex]\[ \boxed{9} \][/tex]
### Dataset 2: [tex]\(8, 24, 7, 8, 15, 10, 13\)[/tex]
- Frequency Count:
- 8 occurs 2 times
- 24 occurs 1 time
- 7 occurs 1 time
- 15 occurs 1 time
- 10 occurs 1 time
- 13 occurs 1 time
Since 8 appears the most frequently (2 times), the mode for this dataset is:
[tex]\[ \boxed{8} \][/tex]
### Dataset 3: [tex]\(4.9, 4, 13, 7, 14, 10, 17\)[/tex]
- Frequency Count:
- 4.9 occurs 1 time
- 4 occurs 1 time
- 13 occurs 1 time
- 7 occurs 1 time
- 14 occurs 1 time
- 10 occurs 1 time
- 17 occurs 1 time
Since each value appears only once, there is no number that repeats. Therefore, we consider the first appearing value in case of a tie:
[tex]\[ \boxed{4.9} \][/tex]
### Dataset 4: [tex]\(3, 5, 7, 5, 9, 7, 5\)[/tex]
- Frequency Count:
- 3 occurs 1 time
- 5 occurs 3 times
- 7 occurs 2 times
- 9 occurs 1 time
Since 5 appears the most frequently (3 times), the mode for this dataset is:
[tex]\[ \boxed{5} \][/tex]
### Dataset 5: [tex]\(20, 23, 27, 26, 19, 23\)[/tex]
- Frequency Count:
- 20 occurs 1 time
- 23 occurs 2 times
- 27 occurs 1 time
- 26 occurs 1 time
- 19 occurs 1 time
Since 23 appears the most frequently (2 times), the mode for this dataset is:
[tex]\[ \boxed{23} \][/tex]
In conclusion, the modes of the given datasets are:
1. [tex]\(2,3,5,6,8,9,9\)[/tex] -> [tex]\( \boxed{9} \)[/tex]
2. [tex]\(8,24,7,8,15,10,13\)[/tex] -> [tex]\( \boxed{8} \)[/tex]
3. [tex]\(4.9,4,13,7,14,10,17\)[/tex] -> [tex]\( \boxed{4.9} \)[/tex]
4. [tex]\(3,5,7,5,9,7,5\)[/tex] -> [tex]\( \boxed{5} \)[/tex]
5. [tex]\(20,23,27,26,19,23\)[/tex] -> [tex]\( \boxed{23} \)[/tex]
