Here is a data set summarized as a stem-and-leaf plot: 
6# | 13444578 
7# | 01334555666889 
8# | 03688 
9# | 002

How many data values are in this data set? 
 

What is the minimum value in the last class? 
ans = 

What is the frequency of the modal class? (Hint, what is the mode?) 
frequency = 

How many of the original values are greater than 70? 
ans = 

Let's analyze the given stem-and-leaf plot:

### Stem-and-Leaf Plot:
6 | 13444578  
7 | 01334555666889  
8 | 03688  
9 | 002  

#### Questions and Solutions:

1. **How many data values are in this data set?**
   - Count all the leaves in the plot.
   - Count:  
     - 6th stem: 8 values  
     - 7th stem: 15 values  
     - 8th stem: 5 values  
     - 9th stem: 3 values  
   - Total number of data values: \(8 + 15 + 5 + 3 = 31\)

   **Answer:** 31

2. **What is the minimum value in the last class?**
   - The "last class" refers to the last stem, which is "9".
   - The minimum value is the smallest leaf in this row, which is "0".
   - Thus, the minimum value in the last class is 90.

   **Answer:** 90

3. **What is the frequency of the modal class?**
   - The modal class is the stem with the most leaves.
   - Stem "7" has the most leaves (15 leaves).
   - Frequency of the modal class: 15

   **Answer:** 15

4. **How many of the original values are greater than 70?**
   - Count the values in the rows where the stem is 7 or greater.
   - Stem "7": 15 values  
   - Stem "8": 5 values  
   - Stem "9": 3 values  
   - Total values greater than 70: \(15 + 5 + 3 = 23\)

   **Answer:** 23

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Would you like more details or have any further questions?

### Additional Questions:
1. What is the range of the data set?
2. What is the median of the data set?
3. What is the maximum value in the data set?
4. How many data values are less than 75?
5. What is the sum of all the values in the dataset?

**Tip:** In a stem-and-leaf plot, the mode can be identified by the stem with the most leaves, indicating where the data is most concentrated.

Explore characteristics and analysis of a stem-and-leaf plot data set, including total data values, minimum value in the last class, frequency of the modal class, and count of values greater than 70. Detailed step-by-step solutions provided.

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