To calculate the mode using the grouping method, follow these steps:

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

In the given table:

The highest frequency is 7, so the modal class is 30 – 35.

2. Apply the formula for mode: $\text{Mode} = L + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h$ Where:

• $L$ = lower boundary of the modal class = 30
• $f_1$ = frequency of the modal class = 7
• $f_0$ = frequency of the class preceding the modal class = 6
• $f_2$ = frequency of the class succeeding the modal class = 3
• $h$ = class width = 5 (the difference between consecutive lower class limits)

Now plug in the values: $\text{Mode} = 30 + \left(\frac{7 - 6}{2(7) - 6 - 3}\right) \times 5$ $\text{Mode} = 30 + \left(\frac{1}{14 - 9}\right) \times 5$ $\text{Mode} = 30 + \left(\frac{1}{5}\right) \times 5$ $\text{Mode} = 30 + 1 = 31$

So, the mode is 31.

Would you like more details on any step? Here are some related questions to expand on this:

1. How is the mode useful in real-life data analysis?
2. Can the mode be used with any type of frequency distribution?
3. What is the significance of the class width in calculating the mode?
4. How do you interpret a distribution where the mode, mean, and median differ significantly?
5. How does the grouping method differ from other methods of finding the mode?

Tip: Always ensure the class intervals are equal when calculating the mode using this formula for accurate results!