https://file.aiquickdraw.com/mathbot/file/1729862385272zwqp04ru.jpg

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?
Frequency - 78,192,425,220,62 Total = 977, Mean = 195.4 now find audience ratings

To find the average rating given by the audience, we will calculate the weighted mean, using the formula:

\[
\text{Average (Mean)} = \frac{\sum (\text{Rating} \times \text{Frequency})}{\sum \text{Frequency}}
\]

From the image, the ratings and their corresponding frequencies are:

- Rating 1: Frequency = 78
- Rating 2: Frequency = 192
- Rating 3: Frequency = 425
- Rating 4: Frequency = 220
- Rating 5: Frequency = 62

Now, we compute the total weighted sum of the ratings:

\[
\text{Weighted Sum} = (1 \times 78) + (2 \times 192) + (3 \times 425) + (4 \times 220) + (5 \times 62)
\]

\[
\text{Weighted Sum} = 78 + 384 + 1275 + 880 + 310 = 2927
\]

The total frequency (already given as 977):

\[
\text{Average Rating} = \frac{2927}{977} \approx 2.9959
\]

So, the average rating given by the audience is approximately **3.00**.

Would you like further details or have any questions about this solution?

Here are 5 related questions for further exploration:
1. What is the median rating in this dataset?
2. How would the mode be identified for the given audience ratings?
3. Can we calculate the standard deviation of these ratings?
4. How does the frequency distribution affect the skewness of this data?
5. What is the percentage of users who rated the movie as 4 or 5?

**Tip:** In a weighted average calculation, multiplying each value by its corresponding frequency ensures that the value with more instances has a higher contribution to the overall mean.

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?

Find the average rating given by the audience on a movie review website using the weighted mean method. The dataset includes ratings 1 to 5 with corresponding frequencies: 78, 192, 425, 220, and 62, resulting in an average rating of approximately 3.00.

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