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
Step 1: The formula for the mean of a grouped frequency distribution is x = ( (f_i · x_i))/(N), where x_i is the class midpoint in hours per week, f_i is the frequency, and N = 200 students. Step 2: Compute the class midpoints x_i in hours per week. x_1 = (0+9)/(2) = 4.5, x_2 = (10+19)/(2) = 14.5, x_3 = (20+29)/(2) = 24.5, x_4 = (30+39)/(2) = 34.5. Step 3: Compute each product f_i · x_i in hours per week. 20 × 4.5 = 90, 50 × 14.5 = 725, 60 × 24.5 = 1470, 70 × 34.5 = 2415. Step 4: Sum the products. (f_i · x_i) = 90 + 725 + 1470 + 2415 = 4700. Step 5: Compute the mean. x = (4700)/(200) = 23.5. The mean is 23.5 hours per week.