Let $$M$$ denote the median of the following frequency distribution.

Then $$20M$$ is equal to :

Step 1: Calculate the Cumulative Frequency ($$CF$$)

To find the median, we first construct a cumulative frequency table:

• Total Frequency ($$N$$): $$36$$

Step 2: Identify the Median Class

The median position is given by:

$$\frac{N}{2} = \frac{36}{2} = 18$$

Look for the first cumulative frequency that is greater than or equal to $$18$$. This value is $$22$$, which corresponds to the class interval $$8 - 12$$.

• Median Class: $$8 - 12$$

Step 3: Apply the Median Formula

The formula for the median of a grouped frequency distribution is:

$$M = L + \left( \frac{\frac{N}{2} - CF_{\text{pre}}}{f} \right) \times h$$

Where:

• $$L$$ (Lower limit of the median class) = $$8$$
• $$\frac{N}{2}$$ = $$18$$
• $$CF_{\text{pre}}$$ (Cumulative frequency of the preceding class) = $$12$$
• $$f$$ (Frequency of the median class) = $$10$$
• $$h$$ (Class width) = $$4$$

Substituting these values into the formula:

$$M = 8 + \left( \frac{18 - 12}{10} \right) \times 4$$  $$M = 8 + \left( \frac{6}{10} \right) \times 4$$  $$M = 8 + 2.4 = 10.4$$

Step 4: Calculate $$20M$$

Now, substitute the value of $$M$$ to find the final answer:

$$20M = 20 \times 10.4 = 208$$

Answer:

208