Question 1: Calculate the midpoint of the class interval 20–30.

Answer: 25

Question 2: Find the midpoints of the class intervals: 10–15, 15–20, and 20–25.

Answer: 12.5, 17.5, 22.5

Question 3: A grouped data table shows ages in ranges: 0–10, 10–20, 20–30. Calculate the midpoints for each range.

Answer: 5, 15, 25

Question 4: Plot the graph of y=2x on the grid. Draw the line and label two points with their coordinates.

Answer: e.g., (1,2), (4,8)

Question 5: Construct a triangle with side lengths 6 cm, 8 cm, and 10 cm on the grid. Label the midpoints of each side.

Answer: Midpoints will be the average of endpoints for each side.

Question 6: A class has the following score ranges and the number of students: 0–10 (5 students), 10–20 (8 students), 20–30 (12 students). Calculate the estimated mean score using midpoints.

Answer: Approximate mean = (midpoints × frequency sum) / total students

Question 7: Explain why using midpoints provides a good estimate of the mean in grouped data. Write your reasoning.

Answer: Midpoints represent the center of each group, giving a reasonable estimate of the average value within each interval.

Question 8: Identify and correct the mistake in this calculation: The midpoint of 30–40 is given as 50.

Answer: The correct midpoint is 35, not 50.

Question 9: A survey classifies data into intervals: 0–20, 20–40, 40–60. The midpoints are used to estimate the mean score. If the midpoints are 10, 30, and 50, and the corresponding frequencies are 4, 6, and 10, calculate the estimated mean.

Answer: (10×4 + 30×6 + 50×10) / (4+6+10) = 30.

Question 10: Describe a real-world scenario where calculating midpoints can help in decision making or data analysis.

Answer: Estimating average age of participants in age groups for community planning.

Question 11: Identify a common mistake students make when calculating midpoints and explain how to avoid it.

Answer: Adding the endpoints instead of averaging them; avoid by always dividing the sum of endpoints by 2.