AP TET Paper 2 Math and Science Model Paper 4

Concept:The median of grouped data is found using the formula:$$\text{Median} = L + \left(\frac{\frac{N}{2} - CF}{f}\right) \times h$$where $L$ is the lower boundary of the median class, $N$ is total frequency, $CF$ is cumulative frequency before the median class, $f$ is median class frequency, and $h$ is class width.Explanation:First, convert the given intervals into regular continuous intervals by subtracting $0.5$ from each lower limit and adding $0.5$ to each upper limit.The regular intervals and cumulative frequencies are shown below:Total frequency, $N = 65$So, $\frac{N}{2} = \frac{65}{2} = 32.5$The cumulative frequency just greater than $32.5$ is $50$, which corresponds to the class $24.5 - 29.5$.Thus, the median class is $24.5 - 29.5$.Here, $L = 24.5$, $CF = 30$, $f = 20$, and $h = 5$.Substitute these values into the median formula:$$\text{Median} = 24.5 + \left(\frac{32.5 - 30}{20}\right) \times 5$$$$\text{Median} = 24.5 + \left(\frac{2.5}{20}\right) \times 5$$$$\text{Median} = 24.5 + 0.625 = 25.125$$Rounded to two decimal places, the median is $25.13$.Answer:Option D: $25.13$