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: Calculate the midpoint for each speed interval. For grouped frequency data, the mean is estimated by using the midpoint of each class interval. • For 0 < v 20, midpoint x_1 = (0+20)/(2) = 10 • For 20 < v 40, midpoint x_2 = (20+40)/(2) = 30 • For 40 < v 45, midpoint x_3 = (40+45)/(2) = 42.5 • For 45 < v 50, midpoint x_4 = (45+50)/(2) = 47.5 • For 50 < v 60, midpoint x_5 = (50+60)/(2) = 55 • For 60 < v 80, midpoint x_6 = (60+80)/(2) = 70 Step 2: Calculate the product of each midpoint and its corresponding frequency (fx). • 10 × 16 = 160 • 30 × 34 = 1020 • 42.5 × 62 = 2635 • 47.5 × 58 = 2755 • 55 × 26 = 1430 • 70 × 4 = 280 Step 3: Calculate the sum of the products ( fx) and the sum of the frequencies ( f). Sum of products fx = 160 + 1020 + 2635 + 2755 + 1430 + 280 = 8280 Sum of frequencies f = 16 + 34 + 62 + 58 + 26 + 4 = 200 (This matches the total of 200 cars given in the question). Step 4: Calculate the estimate of the mean. The formula for the estimated mean is x = ( fx)/( f). x = (8280)/(200) x = 41.4 The estimate of the mean speed is 41.4 km/h. Got more? Send 'em!