The problem presents a grouped frequency table with some incomplete data. To estimate the median using this data, we need to follow the steps for finding the median in a grouped frequency distribution:

Grouped Frequency Distribution Data (incomplete):

• Class 1: $30.00 < 35.00$, $f = 4$, cumulative frequency = 4
• Class 2: $35.00 < 40.00$, $f = 11$, cumulative frequency = 15
• Class 3: $40.00 < 45.00$, $f = A$, cumulative frequency = 43
• Class 4: $45.00 < 50.00$, $f = 17$, cumulative frequency = 60

The total frequency (Σf) is given as 60.

Step-by-Step Solution for the Median:

1. Find the cumulative frequency column: The cumulative frequency is the running total of the frequencies up to that class. It's partially filled out, but we'll calculate it fully:

   • $\text{Class 1:}$ Cumulative Frequency = $4$
   • $\text{Class 2:}$ Cumulative Frequency = $4 + 11 = 15$
   • $\text{Class 3:}$ Cumulative Frequency = $15 + A = 43$, so $A = 43 - 15 = 28$
   • $\text{Class 4:}$ Cumulative Frequency = $43 + 17 = 60$

2. Determine the median class: The median class is the class where the cumulative frequency surpasses $\frac{N}{2}$, where $N = 60$, so $\frac{N}{2} = 30$.

   From the cumulative frequencies:

   • Class 1 cumulative frequency = 4 (less than 30)
   • Class 2 cumulative frequency = 15 (less than 30)
   • Class 3 cumulative frequency = 43 (greater than 30)

   Therefore, the median class is $40.00 < 45.00$.

3. Apply the median formula: The formula for the median is: $\text{Median} = L + \left( \frac{\frac{N}{2} - F}{f} \right) \times h$ Where:

   • $L$ is the lower boundary of the median class ($L = 40.00$)
   • $F$ is the cumulative frequency of the class before the median class ($F = 15$)
   • $f$ is the frequency of the median class ($f = 28$)
   • $h$ is the class width (in this case, $h = 5$, because the width between classes is 5)

4. Substitute values into the formula: $\text{Median} = 40.00 + \left( \frac{30 - 15}{28} \right) \times 5$ Simplifying: $\text{Median} = 40.00 + \left( \frac{15}{28} \right) \times 5$ $\text{Median} = 40.00 + \left( 0.5357 \right) \times 5$ $\text{Median} = 40.00 + 2.6785$ $\text{Median} \approx 42.68$

Since the calculated value of $42.68$ does not match any of the given choices, it seems there might be an error in the question's given options or the assumption of class boundaries. This would require double-checking the problem's data or options.

Would you like me to explore the fm column or recheck any assumptions?