https://file.aiquickdraw.com/mathbot/file/1729432735864m9ix93vh.jpg

To find the **average rating** given by the audience, we need to calculate the **weighted mean** using the ratings and their corresponding frequencies.

Here’s the breakdown from the bar chart:

| Rating (x) | Frequency (f) |
|------------|---------------|
| 1          | 78            |
| 2          | 192           |
| 3          | 425           |
| 4          | 220           |
| 5          | 62            |

### Formula for Average (Weighted Mean):
\[
\bar{x} = \frac{\sum (x \cdot f)}{\sum f}
\]

#### Step 1: Calculate \(x \cdot f\) for each rating
- \(1 \times 78 = 78\)  
- \(2 \times 192 = 384\)  
- \(3 \times 425 = 1275\)  
- \(4 \times 220 = 880\)  
- \(5 \times 62 = 310\)

#### Step 2: Sum of \(x \cdot f\)
\[
78 + 384 + 1275 + 880 + 310 = 2927
\]

#### Step 3: Sum of frequencies (\(\sum f\))
\[
78 + 192 + 425 + 220 + 62 = 977
\]

#### Step 4: Calculate the average rating
\[
\bar{x} = \frac{2927}{977} \approx 2.99
\]

### Final Answer:
The **average rating** given by the audience is approximately **2.99**.

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Would you like further explanation or details? 

Here are 5 related questions you may find helpful:
1. How is weighted mean different from arithmetic mean?
2. What would the median rating be for this data?
3. How can standard deviation of these ratings be calculated?
4. What is the mode of these ratings?
5. How would the average change if the 5-star ratings doubled?

**Tip:** Weighted means are useful when different values contribute unequally to the final result, as in this case with ratings.

The ratings given by the audience on a movie review website for a newly released movie is as shown in Figure 3.2.1. What is the average rating given by audience?

Learn how to calculate the average rating given by the audience for a newly released movie using the weighted mean formula. This step-by-step solution involves analyzing ratings data from a bar chart, suitable for students in Grades 8-10.

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