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find the mean, median and mode. use frequency distribution table. 36 total population 

To find the mean, median, and mode from the data provided:

1. **Data Collection**:
   - **Ages of Actors**: 40, 42, 37, 76, 39, 53, 45, 36, 62, 43, 51, 32, 42, 54, 52, 37, 38, 32, 45, 60, 46, 40, 36, 47, 29, 43, 37, 38, 45, 50, 48, 60, 43, 58, 46, 33.

2. **Mean Calculation**:
   - The mean (average) is calculated by summing all ages and dividing by the total number of actors.

3. **Median Calculation**:
   - The median is the middle value in a list of numbers sorted in ascending order. If there's an even number of observations, the median is the average of the two middle numbers.

4. **Mode Calculation**:
   - The mode is the number that appears most frequently in the data set.

5. **Frequency Distribution Table Creation**:
   - A frequency distribution table will list each unique age along with its frequency of occurrence.

Let's first calculate the mean, median, and then identify the mode by creating a frequency distribution table.The results from the analysis are as follows:

- **Mean**: The average age of the actors is approximately \(44.86\) years.
- **Median**: The median age, which is the middle value when the ages are sorted, is \(43\) years.
- **Mode**: The mode, being the most frequently occurring age among the actors, is \(37\) years.

Here's the frequency distribution table listing each age and its frequency of occurrence:

| Age | Frequency |
|-----|-----------|
| 29  | 1         |
| 32  | 2         |
| 33  | 1         |
| 36  | 2         |
| 37  | 3         |
| 38  | 2         |
| 39  | 1         |
| 40  | 2         |
| 42  | 2         |
| 43  | 3         |
| 45  | 3         |
| 46  | 2         |
| 47  | 1         |
| 48  | 1         |
| 50  | 1         |
| 51  | 1         |
| 52  | 1         |
| 53  | 1         |
| 54  | 1         |
| 58  | 1         |
| 60  | 2         |
| 62  | 1         |
| 76  | 1         |

Would you like to know more about how these statistics are used or have any other questions?

Here are some related questions you might find interesting:
1. How does the shape of the frequency distribution affect the relationship between mean, median, and mode?
2. What are the implications of having multiple modes in a dataset?
3. Can you explain how outliers, like the age of 76, affect the mean?
4. How would the addition or removal of data points impact the median and mode?
5. What other statistical measures could be useful to analyze this data?

**Tip**: When examining a dataset, it's also useful to consider measures of spread such as the range, variance, and standard deviation, to understand the variability within the data.

Find the mean, median, and mode using frequency distribution table. The following are the ages of male actors when they starred in their Oscar-winning Best Actor performances: [40, 42, 37, 76, 39, 53, 45, 36, 62, 43, 51, 32, 42, 54, 52, 37, 38, 32, 45, 60, 46, 40, 36, 47, 29, 43, 37, 38, 45, 50, 48, 60, 43, 58, 46, 33]

Learn how to calculate the mean, median, and mode of actor ages when they starred in Oscar-winning performances using a frequency distribution table. Analyze data using core statistical measures, perfect for students in Grades 9-12.

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