Question 1: Explain briefly what an S-curve represents in a cumulative frequency graph.

Answer: An S-curve shows the cumulative data increasing slowly at first, then rapidly, and then slowly leveling off, indicating a gradual change over time.

Question 2: Given the cumulative frequency data: 10, 25, 40, 55, 65 for class intervals, plot the approximate S-curve on the grid.

Answer: Student plots a smooth S-shaped curve passing through points (assuming cumulative data vs class interval).

Question 3: Calculate the approximate median class from a cumulative frequency table: Class 1 (0-10), CF=5; Class 2 (10-20), CF=15; Class 3 (20-30), CF=25. Total CF=25.

Answer: Class 2 (10-20) is median since CF just exceeds half of total (12.5).

Question 4: Describe the key features of an S-curve in the context of a cumulative frequency graph.

Answer: Features include a slow start, rapid increase in the middle, and a plateau at the end.

Question 5: Plot the graph of y=2x and draw a smooth S-curve that fits the data points (x, y) = (1,2), (3,6), (5,10).

Answer: Student plots the parabola and sketches a smooth S-shape passing through these points.

Question 6: A dataset shows the cumulative frequency reaching 50 at 12.5 units of time. What is the median time? Show your working.

Answer: Median time is 12.5 units (since CF=50 at 12.5 units).

Question 7: A student incorrectly plots the S-curve as a straight line. Identify and explain the mistake.

Answer: Incorrect because an S-curve should be smooth and sigmoidal, not a straight line that misrepresents the data's gradual change.

Question 8: Using the cumulative frequency table: 5, 15, 35, 55, 70, determine the point where the curve begins to level off. Justify your answer.

Answer: Leveling off begins after CF=55, as the increases become smaller, indicating the curve flattens.

Question 9: Given the data points for a cumulative frequency graph, draw the extension of the S-curve beyond the current data range and explain its significance.

Answer: The extension continues the trend, showing the data reaching a maximum or saturation point, indicating the end of the data distribution.

Question 10: Identify a common mistake when students attempt to draw the S-curve and suggest a method to avoid it.

Answer: Common mistake: drawing a jagged or angular curve instead of a smooth sigmoid shape. To avoid this, students should plot key points and sketch a smooth, continuous curve.