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

Answer: 25

Question 2: A grouped frequency table shows the class intervals 0–10, 10–20, 20–30, with frequencies 5, 8, and 12 respectively. Calculate the midpoints for each interval.

Answer: 5, 15, 25

Question 3: Explain why midpoints are useful when estimating the mean of grouped data.

Answer: Midpoints approximate the value within each class interval, allowing calculation of an estimated mean by treating data as if all values in a class are at its midpoint.

Question 4: Given the class intervals 30–40 and 40–50 with frequencies 7 and 13 respectively, find the estimated mean using midpoints.

Answer: Estimated mean = (35×7 + 45×13) / (7+13) = (245 + 585) / 20 = 830/20 = 41

Question 5: Plot the graph of y=2x for x-values from 0 to 10 on the grid.

Answer: Students will plot points (0,0), (1,2), (2,4), ..., (10,20).

Question 6: Construct a triangle with sides of lengths 4, 6, and 8 units on the grid. Ensure the triangle is valid.

Answer: Students draw a triangle with the specified side lengths, ensuring the triangle inequality holds.

Question 7: A class interval is 50–60 with a frequency of 10. Find the midpoint and explain its significance in estimating data.

Answer: Midpoint = 55. It represents the center of the class interval, used to estimate the data value within that class.

Question 8: An error in calculating midpoints is to add the class limits and divide by 2. Why is this correct or incorrect?

Answer: It is correct because the midpoint of a class interval is always the average of the lower and upper limits.

Question 9: Calculate the midpoints for the class intervals: 0–5, 5–10, 10–15, 15–20.

Answer: 2.5, 7.5, 12.5, 17.5

Question 10: A grouped frequency table lists class intervals 10–20, 20–30, 30–40 with frequencies 3, 6, 9. Calculate the estimated mean using midpoints.

Answer: Estimated mean = (15×3 + 25×6 + 35×9) / (3+6+9) = (45 + 150 + 315) / 18 = 510/18 ≈ 28.33

Question 11: Identify and correct the mistake: When calculating midpoints, students sometimes add the class limits and divide by 2, but they forget to ensure the class limits are correctly identified.

Answer: They should verify the class limits are correct and correctly identify the lower and upper bounds before averaging.