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: Complete the cumulative frequency table. To complete the cumulative frequency table, we need the original frequencies. Based on the previous question (mean calculation), the frequencies are: • 0 < v 20: 16 • 20 < v 40: 34 • 40 < v 45: 62 • 45 < v 50: 58 • 50 < v 60: 26 • 60 < v 80: 4 Now, calculate the cumulative frequencies: • For v 20: 16 (Given) • For v 40: 16 + 34 = 50 (Given) • For v 45: 50 + 62 = 112 • For v 50: 112 + 58 = 170 • For v 60: 170 + 26 = 196 (Given) • For v 80: 196 + 4 = 200 (Given) b) i) The completed cumulative frequency table is: Speed (v km/h) | Cumulative frequency ----------------|--------------------- v 20 | 16 v 40 | 50 v 45 | 112 v 50 | 170 v 60 | 196 v 80 | 200 Step 2: Draw the cumulative frequency diagram. To draw the cumulative frequency diagram, plot the upper class boundary against the cumulative frequency. The points to plot are: • (0, 0) (starting point) • (20, 16) • (40, 50) • (45, 112) • (50, 170) • (60, 196) • (80, 200) ii) On the grid: 1. Plot the points listed above. 2. The x-axis (Speed) ranges from 0 to 80, with each small square representing 1 km/h. 3. The y-axis (Cumulative frequency) ranges from 0 to 200, with each small square representing 2 units of frequency. 4. Draw a smooth curve connecting these points, starting from (0,0). That's 2 down. 3 left today — send the next one.