Let's solve the first part of the problem:

Finding the Median

The first part of the question asks to find the median from the following distribution:

Step 1: Calculate Total Frequency (N)

To find the median, we need to first calculate the total frequency ($N$):

$N = 12 + 18 + 16 + 15 + 6 + 10 + 2 = 79$

Step 2: Find the Median Class

The median is located at the position:

$\frac{N+1}{2} = \frac{79+1}{2} = 40 \text{th} observation$

Now, we need to find in which class the 40th observation lies by summing up the cumulative frequencies:

• Cumulative frequency up to size 18: $12$
• Cumulative frequency up to size 20: $12 + 18 = 30$
• Cumulative frequency up to size 21: $30 + 16 = 46$

So, the 40th observation lies in the class where size = 21.

Step 3: Median

Since the 40th observation lies in the class size 21, the median is 21.

Would you like more details on the calculation process?

Here are 5 related questions to further explore the topic:

1. How is the median different from the mean in grouped data?
2. What steps would you take to calculate the mode for this distribution?
3. How do we handle data that includes decimals in frequency or size values?
4. What if two sizes share the same frequency—how would you determine the median?
5. How does the median change if the highest size value (24) had a frequency of 10 instead of 2?

Tip: The median is less sensitive to outliers in a data set compared to the mean, making it a better measure of central tendency for skewed distributions.