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.