Median

Given, the total frequency and the median is 42.6. We need to calculate the values of and .
- First, we calculate the cumulative frequency distribution:
Since , we have the equation:
Simplifying:
- Next, we use the formula for median in a grouped frequency distribution:
Where: - = lower boundary of the median class = 40
- = total frequency = 685
- = cumulative frequency of the class before the median class = 180 + f_1
- = frequency of the median class = 180
- = class width = 10
We are given that the median is 42.6. Substituting the known values into the median formula:
Simplifying the equation:
We round it to the nearest integer:
- Substituting into equation (1):
Thus, the corrected values are and . Therefore, the correct answer is .