Figure 3.1.G shows a stem and leaf plot of the ratings (out of 100 ) of an actor's performance in different movies.

StemLeaf

4

4

5

2 3 6

6

8

7

8

0 1 3 9 9

9

0

Figure 3.1.G: Performance rating of an actor.
Here 6 | 4 means Rating of 64What is the median rating, if 2 points are added to all of his ratings and then converted to 30 points. (Correct up to 2 decimal point accuracy.)

To determine the median rating after modifying the original data, we'll follow these steps:

1. **List the original data in ascending order.**
2. **Add 2 points to each rating.**
3. **Convert the new ratings to a 30-point scale.**
4. **Find the median of the converted ratings.**

### Step 1: List the Original Data
From the stem and leaf plot, we list the ratings:
- From stem 4: 44
- From stem 5: 52, 53, 56
- From stem 6: 68
- From stem 8: 80, 81, 83, 89, 89
- From stem 9: 90

In ascending order, we have:

\[ 44, 52, 53, 56, 68, 80, 81, 83, 89, 89, 90 \]

### Step 2: Add 2 Points to Each Rating
Adding 2 points to each rating, we get:

\[ 46, 54, 55, 58, 70, 82, 83, 85, 91, 91, 92 \]

### Step 3: Convert the Ratings to a 30-Point Scale
The conversion formula from a 100-point scale to a 30-point scale is:

\[ \text{Converted Rating} = \left( \frac{\text{New Rating}}{100} \right) \times 30 \]

Applying this to each new rating:

\[ 46 \rightarrow \left( \frac{46}{100} \right) \times 30 = 13.80 \]
\[ 54 \rightarrow \left( \frac{54}{100} \right) \times 30 = 16.20 \]
\[ 55 \rightarrow \left( \frac{55}{100} \right) \times 30 = 16.50 \]
\[ 58 \rightarrow \left( \frac{58}{100} \right) \times 30 = 17.40 \]
\[ 70 \rightarrow \left( \frac{70}{100} \right) \times 30 = 21.00 \]
\[ 82 \rightarrow \left( \frac{82}{100} \right) \times 30 = 24.60 \]
\[ 83 \rightarrow \left( \frac{83}{100} \right) \times 30 = 24.90 \]
\[ 85 \rightarrow \left( \frac{85}{100} \right) \times 30 = 25.50 \]
\[ 91 \rightarrow \left( \frac{91}{100} \right) \times 30 = 27.30 \]
\[ 91 \rightarrow \left( \frac{91}{100} \right) \times 30 = 27.30 \]
\[ 92 \rightarrow \left( \frac{92}{100} \right) \times 30 = 27.60 \]

### Step 4: Find the Median of the Converted Ratings
We list the converted ratings in ascending order:

\[ 13.80, 16.20, 16.50, 17.40, 21.00, 24.60, 24.90, 25.50, 27.30, 27.30, 27.60 \]

Since there are 11 ratings, the median is the 6th value:

\[ \text{Median} = 24.60 \]

### Final Answer
The median rating, after adding 2 points to each rating and converting to a 30-point scale, is \( 24.60 \).

Do you want details or have any questions?

Here are 8 related questions that expand on this information:

1. How do you find the median of a data set?
2. What is the significance of converting a data set to a different scale?
3. How does adding a constant value to each data point affect the median?
4. Can you calculate the mean of the converted ratings?
5. What are the steps involved in converting a data set from one scale to another?
6. How would the IQR change if we added a constant to each rating?
7. What is the difference between the median and the mean?
8. How do outliers affect the median compared to the mean?

**Tip:** When converting data from one scale to another, ensure that you apply the conversion formula consistently to maintain the relative differences between data points.

Discover how to calculate the median rating of an actor's performance after adding 2 points to each rating and converting to a 30-point scale. This problem involves statistics and data scaling techniques, suitable for advanced high school students.

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