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To construct the cumulative frequency distribution for the given data, we will progressively add the frequencies as we move through each age group.

Here is the original frequency table:
- 20–29: 27
- 30–39: 37
- 40–49: 14
- 50–59: 3
- 60–69: 5
- 70–79: 1
- 80–89: 2

Now, let's calculate the cumulative frequency:
1. **Less than 30:** 27 (only the first age group)
2. **Less than 40:** 27 + 37 = 64
3. **Less than 50:** 64 + 14 = 78
4. **Less than 60:** 78 + 3 = 81
5. **Less than 70:** 81 + 5 = 86
6. **Less than 80:** 86 + 1 = 87
7. **Less than 90:** 87 + 2 = 89

The cumulative frequency distribution table will be:

| Age (years) of Best Actress when award was won | Cumulative Frequency |
|-----------------------------------------------|----------------------|
| Less than 30                                  | 27                   |
| Less than 40                                  | 64                   |
| Less than 50                                  | 78                   |
| Less than 60                                  | 81                   |
| Less than 70                                  | 86                   |
| Less than 80                                  | 87                   |
| Less than 90                                  | 89                   |

Would you like more details on how this was calculated, or do you have any other questions?

Here are five related questions to expand on this:
1. How can cumulative frequency distributions be used to understand data trends?
2. What is the difference between cumulative frequency and relative cumulative frequency?
3. How would you plot this cumulative frequency distribution on a graph?
4. What insights can be gained by analyzing the cumulative frequency distribution of age groups?
5. How can cumulative frequency help in finding the median of a dataset?

**Tip:** Cumulative frequency is helpful for identifying the number of observations below a particular value in a dataset, aiding in percentile calculations and median identification.

Construct the cumulative frequency distribution for the given data.

Learn how to construct a cumulative frequency distribution for Best Actress age groups using a detailed step-by-step guide. The problem covers core statistical concepts such as cumulative frequency and frequency distributions, suitable for students in Grades 7-10.

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