Let’s analyze the stem-and-leaf plot in the image and answer the questions:

Stem-and-Leaf Plot

• 2#: $022234888$ corresponds to $20, 22, 22, 23, 24, 28, 28, 28$.
• 3#: $001123334568899$ corresponds to $30, 30, 31, 32, 33, 33, 33, 34, 35, 36, 38, 38, 39$.
• 4#: $02566$ corresponds to $40, 42, 45, 46, 46$.
• 5#: $367$ corresponds to $53, 56, 57$.

Step-by-Step Answers:

1. How many data values are in this dataset? Count all the values:

   • 2#: $8$ values
   • 3#: $13$ values
   • 4#: $5$ values
   • 5#: $3$ values
     Total = $8 + 13 + 5 + 3 = 29$.

   Answer: $n = 29$.

2. What is the minimum value in the last class? The last class (stem $5$) contains $53, 56, 57$.
   The minimum value is $53$.

   Answer: $53$.

3. What is the frequency of the modal class? The modal class is the class with the most data values.

   • 2#: $8$ values
   • 3#: $13$ values (modal class)
   • 4#: $5$ values
   • 5#: $3$ values

   The modal class is 3#, and its frequency is $13$.

   Answer: $13$.

4. How many of the original values are greater than 30? Values greater than 30 are from the stems 3#, 4#, and 5#. Count:

   • 3#: $12$ values (excluding $30$)
   • 4#: $5$ values
   • 5#: $3$ values
     Total = $12 + 5 + 3 = 20$.

   Answer: $20$.

Final Answers:

1. $n = 29$
2. $\text{Minimum value in the last class} = 53$
3. $\text{Frequency of the modal class} = 13$
4. $\text{Values greater than 30} = 20$

Would you like additional clarifications or more details?

Related Questions:

1. What is the maximum value in the dataset?
2. How do you calculate the median of this dataset?
3. What percentage of the data falls within the class 3#?
4. How is a stem-and-leaf plot useful for data visualization?
5. What is the range of this dataset?

Tip: When analyzing a stem-and-leaf plot, focus on the stems to identify data intervals and leaves to determine frequencies and specific values.