Question 1: Given the data: Number of books read in a month: 2, 4, 5, 3, 6, 4. Calculate the cumulative frequency for each month and prepare to plot on the graph.

Answer: Cumulative Frequencies: 2, 6, 11, 14, 20, 24

Question 2: Plot the cumulative frequency data: (1, 2), (2, 6), (3, 11), (4, 14), (5, 20), (6, 24). Draw the graph on the provided grid.

Answer: Student draws the cumulative frequency curve properly connecting the points.

Question 3: Explain what the steepness of the curve indicates about the data in question 2.

Answer: A steeper curve indicates a faster accumulation of data, meaning more books read in that period.

Question 4: A new set of data: 3, 5, 7, 4, 6, 8. Calculate the cumulative frequency for each month.

Answer: 3, 8, 15, 19, 25, 33

Question 5: Plot the new cumulative frequency points: (1, 3), (2, 8), (3, 15), (4, 19), (5, 25), (6, 33). Connect the points on the grid.

Answer: Student correctly plots and connects points to form the cumulative frequency curve.

Question 6: Compare the two plotted curves from questions 2 and 5. Which dataset shows faster growth, and why?

Answer: The second dataset grows faster because the curve is steeper, indicating more books read earlier.

Question 7: A graph shows the cumulative frequency increasing from 5 to 15 over a span of 4 units on the x-axis. What is the average rate of increase per unit?

Answer: 2.5

Question 8: Identify and correct the mistake in this plotting process: the student plotted points at (1, 4), (2, 8), (3, 16), (4, 20), but the cumulative frequency at month 3 should be 11, not 16.

Answer: The point at (3, 16) is incorrect; it should be (3, 11).

Question 9: Using the data: 1, 3, 4, 2, 5, 3, calculate the cumulative frequency for each data point.

Answer: 1, 4, 8, 10, 15, 18

Question 10: Construct a cumulative frequency graph to compare two data sets: Set A (2, 4, 6, 8) and Set B (1, 3, 5, 7). Which set reaches a cumulative frequency of 15 first?

Answer: Set A reaches 15 at the last point, Set B reaches 15 earlier.

Question 11: Challenge: Given the cumulative frequency data: 2, 5, 9, 14, 20, 27, 35, plot these points and describe the trend you observe.

Answer: The curve shows increasing growth with accelerating rate, indicating the data is increasing faster over time.