To find the median from the given data, we need to follow these steps:

1. Identify the total frequency (N): Add all the frequencies: $N = 3 + 6 + 8 + 7 + 6 = 30$

2. Locate the median position: The median is the middle value. Since the total frequency $N = 30$, the median will be located at the $\frac{N}{2}$-th and $\frac{N}{2} + 1$-th positions, which are the 15th and 16th values.

3. Find the cumulative frequencies: $\text{Cumulative frequencies} = 3, 9, 17, 24, 30$ The cumulative frequency tells us where each weight class ends.

   • The 15th and 16th values fall in the third class (53-55), because its cumulative frequency is 17.

4. Apply the median formula for grouped dataTo find the median from the given data, we need to follow these steps:

5. Identify the total frequency (N): Add all the frequencies: $N = 3 + 6 + 8 + 7 + 6 = 30$

6. Locate the median position: The median is the middle value. Since the total frequency $N = 30$, the median will be located at the $\frac{N}{2}$-th and $\frac{N}{2} + 1$-th positions, which are the 15th and 16th values.

7. Find the cumulative frequencies: $\text{Cumulative frequencies} = 3, 9, 17, 24, 30$ The cumulative frequency tells us where each weight class ends.

   • The 15th and 16th values fall in the third class (53-55), because its cumulative frequency is 17.

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

   • $L$ is the lower boundary of the median class (in this case, 52.5 for the 53-55 class),
   • $F$ is the cumulative frequency before the median class (in this case, 9),
   • $f$ is the frequency of the median class (in this case, 8),
   • $h$ is the class width (in this case, $55 - 52 = 3$).

9. Plugging in the values: $\text{Median} = 52.5 + \left( \frac{15 - 9}{8} \right) \times 3$ $\text{Median} = 52.5 + \left( \frac{6}{8} \right) \times 3$ $\text{Median} = 52.5 + 0.75 \times 3$ $\text{Median} = 52.5 + 2.25 = 54.75$

So, the median is 54.75 (option e).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do we determine which class is the median class?
2. Why is it important to calculate cumulative frequency when finding the median?
3. What would happen if the total frequency $N$ was odd instead of even?
4. Can you explain how the class width affects the median calculation?
5. How would the median change if we had different frequencies for each class?

Tip: For grouped data, always calculate cumulative frequencies to identify the median class easily.