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To solve for the mode in a grouped frequency distribution (as seen in your image), we use the formula for the mode of grouped dataTo solve for the mode in a grouped frequency distribution (as seen in your image), we use the formula for the mode of grouped 

\[
\text{Mode} = L + \left( \frac{f_1 - f_0}{(f_1 - f_0) + (f_1 - f_2)} \right) \times h
\]

Where:
- \( L \) is the lower boundary of the modal class (the class with the highest frequency).
- \( f_1 \) is the frequency of the modal class.
- \( f_0 \) is the frequency of the class before the modal class.
- \( f_2 \) is the frequency of the class after the modal class.
- \( h \) is the class width.

From the table in the image:
- Modal class is \(71-80\) (highest frequency of 13).
- \( L = 70.5 \) (lower boundary of the modal class).
- \( f_1 = 13 \) (frequency of the modal class).
- \( f_0 = 10 \) (frequency of the class before: \(61-70\)).
- \( f_2 = 5 \) (frequency of the class after: \(81-90\)).
- \( h = 10 \) (class width).

Now let's calculate the mode.The mode of the given grouped frequency distribution is approximately \( 73.23 \). 

This corresponds to option **b. 73.22**.

Do you have any questions or need further clarification? 

Here are 5 related questions to deepen understanding:
1. What is the difference between the mode and the mean in a grouped dataset?
2. How is the median calculated in grouped data?
3. Why is the class width important when calculating the mode?
4. Can a dataset have more than one mode? How does that affect the interpretation?
5. How would you calculate the mode if the data were ungrouped?

**Tip**: Always check for the class with the highest frequency first when identifying the modal class in grouped data.

What is the mode of the grouped frequency distribution provided in the table?

Learn how to calculate the mode of a grouped frequency distribution. This problem involves a step-by-step calculation using the grouped data mode formula. Key concepts include identifying the modal class and calculating the mode using class boundaries and frequencies.

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