This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Krishna, good to see you again. Step 1: Calculate the cumulative frequency (cf) for the given data. | Weight (kg) | Number of students (f) | Cumulative Frequency (cf) | | :---------- | :--------------------- | :------------------------ | | 40-45 | 9 | 9 | | 45-50 | 5 | 9 + 5 = 14 | | 50-55 | 8 | 14 + 8 = 22 | | 55-60 | 9 | 22 + 9 = 31 | | 60-65 | 6 | 31 + 6 = 37 | | 65-70 | 3 | 37 + 3 = 40 | The total number of students, N = 40. Step 2: Determine the median class. The median position is (N)/(2) = (40)/(2) = 20. The cumulative frequency just greater than or equal to 20 is 22, which corresponds to the class interval 50-55. Therefore, the median class is 50-55. Step 3: Identify the values for the median formula. From the median class 50-55: • Lower limit of the median class, L = 50 • Cumulative frequency of the class preceding the median class, cf = 14 • Frequency of the median class, f = 8 • Class size, h = 55 - 50 = 5 • (N)/(2) = 20 Step 4: Apply the median formula for grouped data. The formula for the median is: Median = L + ( (N)/(2) - cff ) × h Step 5: Substitute the values and calculate the median. Median = 50 + ( (20 - 14)/(8) ) × 5 Median = 50 + ( (6)/(8) ) × 5 Median = 50 + ( (3)/(4) ) × 5 Median = 50 + (15)/(4) Median = 50 + 3.75 Median = 53.75 The median weight of the students is 53.75 kg. Send me the next one 📸