The image shows a frequency distribution table, and the question asks for the mode of grouped data. To calculate the mode for grouped data, we can use the following formula:

$\text{Mode} = L_m + \left( \frac{f_1 - f_0}{(f_1 - f_0) + (f_1 - f_2)} \right) \times c$

Where:

• $L_m$ is the lower boundary of the modal class.
• $f_1$ 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.
• $c$ is the class width.

Steps:

1. Identify the modal class: The modal class is the class with the highest frequency. From the table:

   • The modal class is $71-80$, with frequency $f_1 = 13$.

2. Identify the necessary parameters:

   • $L_m = 71$ (the lower boundary of the modal class),
   • $f_0 = 9$ (frequency of the class before the modal class, $61-70$),
   • $f_2 = 8$ (frequency of the class after the modal class, $81-90$),
   • $c = 10$ (the class width, since each interval is of size 10).

Plugging in the values:

$\text{Mode} = 71 + \left( \frac{13 - 9}{(13 - 9) + (13 - 8)} \right) \times 10$ $\text{Mode} = 71 + \left( \frac{4}{4 + 5} \right) \times 10$ $\text{Mode} = 71 + \left( \frac{4}{9} \right) \times 10$ $\text{Mode} = 71 + 4.44$ $\text{Mode} \approx 75.44$

The closest answer to this calculation is c. 75.21.

Would you like further clarification or details on any steps?

Related Questions:

1. How do you calculate the median for grouped data?
2. What is the significance of the mode in statistics?
3. How does the class width affect the mode in grouped data?
4. Can you find the mean of the data from this table?
5. How would the mode change if the highest frequency was in a different class?

Tip:

In frequency distribution, the modal class is always the class interval with the highest frequency, but calculating the exact mode requires the formula to account for data spread within that interval.