Question 1: Calculate the cumulative frequency for the 40-minute mark based on the given data: 10 students took less than 20 minutes, 15 students took less than 30 minutes, and 20 students took less than 40 minutes.

Answer: 20

Question 2: Using the cumulative frequency data: 5 students less than 10 min, 12 less than 20 min, 18 less than 30 min, draw the cumulative frequency graph on the grid. Label axes appropriately.

Answer: Graph drawn correctly reflecting data points at (10,5), (20,12), (30,18).

Question 3: Construct a cumulative frequency polygon for the data: 8 students less than 15 min, 14 less than 25 min, 20 less than 35 min, 25 less than 45 min.

Answer: Polygon with vertices at (15,8), (25,14), (35,20), (45,25).

Question 4: In a survey, 12 students completed a test in less than 15 minutes, 20 in less than 30 minutes, and 30 in less than 45 minutes. Plot the cumulative frequency graph and interpret what the shape indicates about the data distribution.

Answer: Graph plotted with points at (15,12), (30,20), (45,30). The shape suggests a steady increase in students completing the test faster.

Question 5: A class's test scores are grouped with the following cumulative frequencies: score <50: 5 students, <60: 12 students, <70: 20 students, <80: 25 students. Plot these on the grid and determine the median score.

Answer: Plot points at (50,5), (60,12), (70,20), (80,25). Median approximately at score 65 based on the data.

Question 6: The cumulative frequency data for ages of participants: 10, 18, 25, 32, 36, 40. Plot these points and describe how the graph can be used to estimate median age.

Answer: Points at (age, cumulative frequency): (20,10), (30,18), (40,25), (50,32), (60,36), (70,40). Median age near 40, as the middle value of 40 data points is around 40 years.

Question 7: Given the cumulative frequency data: 6, 12, 18, 24, 30, draw the graph and identify at which cumulative frequency the median lies.

Answer: Graph with points at (x, y): (1,6), (2,12), (3,18), (4,24), (5,30). Median at cumulative frequency 15 (between 12 and 18).

Question 8: A sports event records the number of spectators arriving before each half-hour interval. Data: 50, 120, 190, 250, 300. Plot the cumulative frequency and interpret the trend.

Answer: Plot points at (30,50), (60,120), (90,190), (120,250), (150,300). The increasing trend indicates growing spectator attendance over time.

Question 9: Identify and correct the mistake in the following plotting instruction: 'Plot points at (20,5), (40,10), (60,15), (80,20), but label axes as 'Time (minutes)' and 'Number of students'.'

Answer: No mistake; axes labeled correctly and points plotted correctly. Alternatively, if axes not scaled properly, fix the scale to match data points.

Question 10: Challenge: Given the data points (10,8), (20,15), (30,22), (40,28), (50,33), draw the cumulative frequency graph and estimate the approximate number of students who took less than 25 minutes.

Answer: Graph with points at (10,8), (20,15), (30,22), (40,28), (50,33). The estimated students less than 25 min are about 15, between the points at 20 and 30.

Question 11: Mixed Review: Plot the points for cumulative frequency data: 3, 7, 12, 18, 25. Connect these points and explain how the shape of the graph helps in understanding the data.

Answer: Points at (x, y): (1,3), (2,7), (3,12), (4,18), (5,25). The increasing slope indicates more students are completing the task as time progresses.