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The following steps can determine the median of the grouped frequency distribution:

1. Find the cumulative frequency distribution and denote $$N$$ as the total frequency.

2. Find the $$\frac{N}{2}^{th}$$ term.

3. The class which contains the cumulative frequency $$\frac{N}{2}$$ is the median class.

4. The median of the class can be determined using the formula:

Median $$= l + \frac{(\frac{N}{2} - m)}{f} \times c$$

Where $$l$$ is the lower limit of the median class,

$$m$$ is the cumulative frequency of the class preceeding the median class,

$$f$$ is the frequency of the median class,

$$c$$ is the width of the median class, and

$$N$$ is the total frequency.
Example:
Find the median of the following data.

 Class interval $$100 - 200$$ $$200 - 300$$ $$300 - 400$$ $$400 - 500$$ Frequency $$30$$ $$15$$ $$26$$ $$44$$

Solution:

 Class interval Frequency Cumulative frequency $$100 - 200$$ $$30$$ $$30$$ $$200 - 300$$ $$15$$ $$45$$ $$300 - 400$$ $$26$$ $$71$$ $$400 - 500$$ $$44$$ $$115$$

Therefore, the total frequency is $$N = 115$$.

Median class $$= (\frac{N}{2}^{th})$$ value

$$= (\frac{115}{2})^{th}$$ value

$$= (57.5)^{th}$$ value
The median of the grouped frequency distribution can be determined using the formula $$l + \frac{(\frac{N}{2} - m)}{f} \times c$$
The value $$57.5$$ lies in the class interval $$300 - 400$$

Here, $$l = 300$$, $$\frac{N}{2} = 57.5$$, $$m = 45$$, $$f = 26$$ and $$c = 100$$

Substituting the known values in the above formula, we have:

Median $$= 300 + (\frac{57.5 - 45}{26}) \times 100$$

$$= 300 + (0.481) \times 100$$

$$= 300 + 48.1$$

$$= 348.1$$

Therefore, the median of the given data is $$348.1$$