Telangana TET Paper 2 Math and Science Model Paper 4

Concept:The median for grouped data is found using the formula $Median = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \times h$, where $L$ is the lower boundary of the median class, $N$ is total frequency, $CF$ is cumulative frequency before the median class, $f$ is frequency of the median class, and $h$ is class width. Since the given class intervals are discontinuous, first convert them into continuous ones by subtracting 0.5 from each lower limit and adding 0.5 to each upper limit.Explanation:Make the intervals continuous: the new intervals are 9.5–14.5, 14.5–19.5, 19.5–24.5, 24.5–29.5, 29.5–34.5, 34.5–39.5. Create the cumulative frequency table:Total frequency $N = 65$. So $N/2 = 32.5$. The cumulative frequency just greater than 32.5 is 50, so the median class is $24.5 - 29.5$. For this class, $L = 24.5$, $CF = 30$, $f = 20$, and $h = 5$. Substitute into the formula: $Median = 24.5 + \left( \frac{32.5 - 30}{20} \right) \times 5 = 24.5 + \left( \frac{2.5}{20} \right) \times 5 = 24.5 + 0.125 \times 5 = 24.5 + 0.625 = 25.125 \approx 25.13$.Answer:Option D: 25.13