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
To find the mean using an assumed mean, we use the formula: x = A + ( f_i d_i)/( f_i) where A is the assumed mean, f_i is the frequency, and d_i = x_i - A is the deviation of each data point x_i from the assumed mean. Step 1: Identify the given data and the assumed mean. The weights (x_i) are 50 kg, 54 kg, 62 kg, and 65 kg. The number of men (f_i) for each weight are 15, 20, 25, and 30, respectively. The assumed mean (A) is 55 kg. Step 2: Create a table to calculate d_i and f_i d_i. | x_i (Weight in kg) | f_i (No. of men) | d_i = x_i - 55 | f_i d_i | |----------------------|--------------------|-------------------|------------| | 50 | 15 | 50 - 55 = -5 | 15 × (-5) = -75 | | 54 | 20 | 54 - 55 = -1 | 20 × (-1) = -20 | | 62 | 25 | 62 - 55 = 7 | 25 × 7 = 175 | | 65 | 30 | 65 - 55 = 10 | 30 × 10 = 300 | Step 3: Calculate the sum of frequencies ( f_i) and the sum of f_i d_i ( f_i d_i). f_i = 15 + 20 + 25 + 30 = 90 f_i d_i = -75 - 20 + 175 + 300 = -95 + 175 + 300 = 80 + 300 = 380 Step 4: Apply the formula for the mean. x = A + ( f_i d_i)/( f_i) x = 55 + (380)/(90) x = 55 + (38)/(9) x = 55 + 4.222... x = 59.222... Rounding to two decimal places, the mean weight is 59.22 kg. The mean weight is 59.22 kg. Drop the next question.