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The image shows a table with intervals and their corresponding frequencies and asks for the step to determine the mode \( M_o \) of the data. Let's walk through the calculation of the mode for grouped data.

### Steps to find the mode:
The formula for calculating the mode for grouped data is:

\[
M_o = L + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times w
\]

Where:
- \( L \) is the lower boundary of the modal class (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.
- \( w \) is the class width (difference between the upper and lower boundaries of any class).

### Analyzing the table:
- The modal class is 81–85, as it has the highest frequency (13).
- \( L = 80.5 \) (the lower boundary of the class 81–85).
- \( f_1 = 13 \) (frequency of the modal class).
- \( f_0 = 6 \) (frequency of the class before: 76–80).
- \( f_2 = 11 \) (frequency of the class after: 86–90).
- The class width \( w = 5 \).

### Calculation:
Substitute these values into the mode formula:

\[
M_o = 80.5 + \left(\frac{13 - 6}{2(13) - 6 - 11}\right) \times 5
\]

Simplify:

\[
M_o = 80.5 + \left(\frac{7}{26 - 17}\right) \times 5 = 80.5 + \left(\frac{7}{9}\right) \times 5
\]

Now, calculate the result:

\[
M_o = 80.5 + \frac{35}{9} \approx 80.5 + 3.89 = 84.39
\]

Thus, the correct step is the formula \( M_o = 80.5 + \frac{35}{9} \), which corresponds to **Option A**.

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Would you like further explanation or details on this calculation?

Here are five related questions to extend your understanding:
1. What is the difference between mode, mean, and median in statistics?
2. How do you find the mean for grouped data?
3. What is the significance of the mode in a data set?
4. How would the calculation change if the class widths were unequal?
5. Can mode always be determined for every type of data distribution?

**Tip**: When dealing with grouped data, always double-check the class with the highest frequency—it indicates the modal class!

Determine the mode from the given frequency distribution table and select the correct formula.

Learn how to calculate the mode for grouped data using the formula Mo = L + (f1 - f0) / (2f1 - f0 - f2) * w. This example demonstrates calculating the mode based on a frequency table with class intervals and frequencies, suitable for students in Grades 10-12.

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