It seems that you have shared a stem-and-leaf plot regarding an actor's performance ratings. I will first address the question you asked about the median rating if 2 points are added to each rating and then converted to a 20-point scale.

Step-by-Step Process for Question 9:

1. Extract the Data from the Stem-and-Leaf Plot: The stem-and-leaf plot shows the following ratings:

   • 46 (stem 4, leaf 6)
   • 50, 51, 52, 53 (stem 5, leaf 0, 1, 2, 3)
   • 60, 62, 63, 67, 68 (stem 6, leaf 0, 2, 3, 7, 8)
   • 76 (stem 7, leaf 6)
   • 83, 83 (stem 8, leaf 3, 3)

   The full list of ratings is:
   46, 50, 51, 52, 53, 60, 62, 63, 67, 68, 76, 83, 83

2. Add 2 Points to Each Rating: If 2 points are added to each rating, we get the following new values:

   • 48, 52, 53, 54, 55, 62, 64, 65, 69, 70, 78, 85, 85

3. Convert to 20-Point Scale: To convert the ratings to a 20-point scale, we divide each rating by 5:

   • $\frac{48}{5} = 9.6$
   • $\frac{52}{5} = 10.4$
   • $\frac{53}{5} = 10.6$
   • $\frac{54}{5} = 10.8$
   • $\frac{55}{5} = 11.0$
   • $\frac{62}{5} = 12.4$
   • $\frac{64}{5} = 12.8$
   • $\frac{65}{5} = 13.0$
   • $\frac{69}{5} = 13.8$
   • $\frac{70}{5} = 14.0$
   • $\frac{78}{5} = 15.6$
   • $\frac{85}{5} = 17.0$
   • $\frac{85}{5} = 17.0$

4. Find the Median: The ordered ratings on the 20-point scale are:

   • 9.6, 10.4, 10.6, 10.8, 11.0, 12.4, 12.8, 13.0, 13.8, 14.0, 15.6, 17.0, 17.0

   The median is the middle value. Since there are 13 ratings, the median is the 7th value in the ordered list: 12.8.

Conclusion:

The median rating after adding 2 points to each rating and converting to a 20-point scale is 12.8.

Would you like further explanations or help with other parts of the question, such as calculating the interquartile range (IQR)?

Here are some additional related questions:

1. How do you calculate the first quartile (Q1) and third quartile (Q3)?
2. What steps would you take to calculate the interquartile range (IQR) in a dataset?
3. How does adding a constant value to each data point affect the median and other measures of central tendency?
4. What is the difference between a stem-and-leaf plot and a box plot?
5. How can you use a stem-and-leaf plot to find the range of a dataset?

Tip: When converting values to a smaller scale (like from 100 to 20), make sure to divide each value by the appropriate factor to maintain the correct proportion.