Calculate the median for the given frequency distribution.

To estimate the median of a frequency distribution, we follow these steps: Step 1: Calculate the total frequency (N). The total frequency is the sum of all frequencies: N = 6 + 15 + 20 + 7 + 2 = 50 Step 2: Determine the position of the median. The median position is given by (N)/(2): Median position = (50)/(2) = 25 This means the median is the 25th value in the ordered data. Step 3: Identify the median class. We need to find the class interval where the 25th value falls. We do this by calculating the cumulative frequencies: • For class 1-5: Cumulative frequency = 6 • For class 6-10: Cumulative frequency = 6 + 15 = 21 • For class 11-15: Cumulative frequency = 21 + 20 = 41 Since the 25th value is greater than 21 and less than or equal to 41, the median class is 11-15. Step 4: Identify the components for the median formula. The formula for the median of grouped data is: Median = L + ( (N)/(2) - cf_bf_m ) × c Where: • L = Lower class boundary of the median class. For the class 11-15, the lower boundary is 10.5 (midpoint between 10 and 11). • (N)/(2) = Median position = 25. • cf_b = Cumulative frequency of the class before the median class. This is the cumulative frequency for the 6-10 class, which is 21. • f_m = Frequency of the median class. For the 11-15 class, f_m = 20. • c = Class width of the median class. For the class 11-15, the width is 15 - 11 + 1 = 5. (Alternatively, 15.5 - 10.5 = 5). Step 5: Substitute the values into the formula and calculate the median. Median = 10.5 + ( (25 - 21)/(20) ) × 5 Median = 10.5 + ( (4)/(20) ) × 5 Median = 10.5 + ( (1)/(5) ) × 5 Median = 10.5 + 1 Median = 11.5 Comparing this result with the given options: A. 10 (1)/(2) = 10.5 B. 12 C. 13 D. 11 (1)/(2) = 11.5 The calculated median is 11.5, which corresponds to option D. The final answer is D. 11 (1)/(2).