Median Cf Table B549A7

1. **Stating the problem:** We need to calculate the median of a grouped frequency distribution using the cumulative frequency (c.f.) table and the standard median formula. 2. **Formula for median:** $$\text{Median} = L + \left(\frac{\frac{N}{2} - F}{f}\right) \times h$$ where: - $L$ = lower boundary of the median class - $N$ = total frequency - $F$ = cumulative frequency before the median class - $f$ = frequency of the median class - $h$ = class width 3. **Steps to calculate median:** - Construct the cumulative frequency (c.f.) table from the given frequency distribution. - Find the total frequency $N$. - Determine $\frac{N}{2}$. - Identify the median class as the class whose cumulative frequency is just greater than or equal to $\frac{N}{2}$. - Extract $L$, $F$, $f$, and $h$ from the table. - Substitute these values into the median formula. - Calculate the median. 4. **Explanation:** The median class is the class interval where the middle value lies when all data are arranged in order. The formula adjusts the lower boundary by the proportion of the distance into the median class where the median lies. 5. **Example (if data were provided):** - Suppose the cumulative frequency just before the median class is $F=30$, the frequency of the median class is $f=20$, the class width $h=10$, the lower boundary $L=40$, and total frequency $N=100$. - Then $\frac{N}{2} = 50$. - Median = $$40 + \left(\frac{50 - 30}{20}\right) \times 10 = 40 + (1) \times 10 = 50$$. This method can be applied to any grouped frequency distribution once the cumulative frequency table is constructed.