To calculate the median from this grouped frequency distribution, we need to follow these steps:

Given Data:

Step-by-Step Median Calculation:

1. Total Frequency (Σf): Add up all the frequencies: $\text{Total Frequency} = 2 + 8 + 12 + 20 = 42$

2. Cumulative Frequency: We calculate the cumulative frequencies to determine the class containing the median.

   • For the interval 16 – 20: $\text{Cumulative Frequency} = 2$
   • For the interval 21 – 25: $\text{Cumulative Frequency} = 2 + 8 = 10$
   • For the interval 26 – 30: $\text{Cumulative Frequency} = 10 + 12 = 22$
   • For the interval 31 – 35: $\text{Cumulative Frequency} = 22 + 20 = 42$

3. Median Class: The median is located at the position: $\frac{n}{2} = \frac{42}{2} = 21$ The class interval containing the 21st value is 26 – 30 because the cumulative frequency of 22 includes the 21st data point.

4. Median Formula: $\text{Median} = L + \left( \frac{\frac{n}{2} - F}{f} \right) \times h$ Where:

   • $L$ = Lower boundary of the median class = 25.5 (since 26 – 30, subtract 0.5)
   • $F$ = Cumulative frequency before the median class = 10
   • $f$ = Frequency of the median class = 12
   • $h$ = Class width = 30 - 25 = 5
   • $n$ = Total frequency = 42

5. Substitute Values: $\text{Median} = 25.5 + \left( \frac{21 - 10}{12} \right) \times 5$ $= 25.5 + \left( \frac{11}{12} \right) \times 5$ $= 25.5 + 0.9167 \times 5$ $= 25.5 + 4.5833$ $\text{Median} = 30.08$

Therefore, the median of the data is approximately 30.08.

Would you like further clarification or details on this calculation? Here are five related questions you might find helpful:

1. What is the difference between median and mean in grouped data?
2. How would the result change if we added a new class with additional data?
3. What is the significance of the cumulative frequency in calculating the median?
4. Can the class width impact the result of the median calculation?
5. How do you calculate quartiles from a grouped frequency table?

Tip: When dealing with grouped data, always check the cumulative frequency to find which class contains the median!