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From the image, it looks like you're working on a cumulative frequency and histogram problem that includes both a graph and some related tables. Here's a breakdown of the key tasks on your worksheet:

1. **Fill in the cumulative frequency table**: 
   - The first task asks you to complete a table of cumulative frequencies based on class intervals.
   - For example, if the first class is "0 ≤ x < 5" and its frequency is 10, the cumulative frequency for that class would be 10.
   - You would then continue adding up the frequencies for the next classes, leading to values like 30, 57, etc., as shown on the right side of your paper.

2. **Estimating the average (mean)**:
   - The question asks you to estimate the mean of a frequency distribution.
   - This is typically done using the midpoint of each class and multiplying it by the corresponding frequency. Then, sum all those products and divide by the total frequency.

3. **Modal month and finding the mode**:
   - The mode is the class interval with the highest frequency. However, you are asked to explain why you "cannot literally find the mode" in part c, and the answer written seems to indicate that it's because the intervals are different sizes, which complicates the mode calculation.

4. **Percentile and median marks**:
   - You are also asked to find the percentile and the median mark, which can be determined from the cumulative frequency graph.

Would you like help solving any specific part of this exercise? Feel free to ask if you'd like more details on how to calculate the mean, percentile, or anything else!

Here are 5 follow-up questions based on this work:
1. How do you calculate the midpoint for each class interval in a frequency distribution?
2. How do you determine the median using cumulative frequency?
3. Why is the mode more complicated to find when class intervals are unequal?
4. What is the difference between cumulative frequency and relative frequency?
5. How can you visually interpret the 75th percentile using the cumulative frequency graph?

**Tip**: When working with grouped data, always ensure you correctly identify midpoints for classes and account for the class width when finding estimates for the mean or median.

How to solve a cumulative frequency and histogram problem, including filling tables and estimating average, mode, and median?

This problem involves filling cumulative frequency tables, estimating the mean, median, and mode, and understanding percentiles through graphical representation. It is suitable for students in grades 9-12, covering essential statistics concepts.

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