To approximate the mean of a grouped frequency distribution table (GFDT), we use the formula:

$\text{Mean} = \frac{\sum f \cdot x}{\sum f}$

Where:

• $f$ is the frequency of each class.
• $x$ is the midpoint of each class, calculated as $\frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2}$.

Step 1: Calculate the midpoint $x$ for each class.

Class Interval	Frequency $f$	Midpoint $x$
30 - 34	13	$\frac{30 + 34}{2} = 32$
35 - 39	16	$\frac{35 + 39}{2} = 37$
40 - 44	12	$\frac{40 + 44}{2} = 42$
45 - 49	11	$\frac{45 + 49}{2} = 47$
50 - 54	7	$\frac{50 + 54}{2} = 52$
55 - 59	7	$\frac{55 + 59}{2} = 57$
60 - 64	4	$\frac{60 + 64}{2} = 62$
65 - 69	1	$\frac{65 + 69}{2} = 67$
70 - 74	1	$\frac{70 + 74}{2} = 72$

Step 2: Multiply the midpoint $x$ by the frequency $f$ for each class.

$f \cdot x = \text{Frequency} \times \text{Midpoint}$

Step 3: Sum $f \cdot x$ and $f$.

Now, let's compute these values.The approximate mean for the given grouped frequency distribution is $44.2$ (accurate to one decimal place).

Would you like more details or have any questions about this? Here are some related questions for further exploration:

1. How is the mean influenced by changes in frequency values?
2. What would be the effect on the mean if we added more intervals?
3. How does the mean compare to the median and mode in a grouped data set?
4. Can the mean be used to identify skewness in this distribution?
5. What is the relationship between the class width and the accuracy of the mean?

Tip: In grouped data, the midpoint represents the average of each class interval, helping to approximate the mean accurately.