To approximate the mean for a grouped frequency distribution table (GFDT), we need to calculate the midpoint of each class interval and then use those midpoints to find the weighted mean.

Here are the steps to approximate the mean:

1. Find the Midpoint of Each Class Interval:

$\text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$

2. Multiply Each Midpoint by the Corresponding Frequency:

$\text{Midpoint} \times \text{Frequency}$

3. Sum All the Products from Step 2.

4. Sum All the Frequencies.

5. Calculate the Mean:

$\text{Mean} = \frac{\text{Sum of (Midpoint} \times \text{Frequency)}}{\text{Total Frequency}}$

Let's compute the mean using these steps.

Step-by-Step Calculation:

1. Calculate the midpoint for each class interval.
2. Multiply each midpoint by its corresponding frequency.
3. Sum these values to get the total.

Let's perform these calculations now.The approximate mean for the given grouped frequency distribution table is 62.6 (accurate to one decimal place).

Would you like more details on this calculation or have any further questions?

Related Questions:

1. How do you compute the median for a grouped frequency distribution?
2. What is the importance of the midpoint in calculating the mean for grouped data?
3. How do you handle intervals with different class widths in a GFDT?
4. What is the impact of outliers in a frequency distribution?
5. How can we approximate the standard deviation for grouped data?

Tip: When approximating the mean for grouped data, always ensure the midpoints are accurate, as they represent the central value for each interval.