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

Answer: 25

Question 2: Find the midpoints for the class intervals: 0–10, 10–20, 20–30.

Answer: ["5","15","25"]

Question 3: A grouped frequency table shows class intervals 40–50, 50–60, 60–70 with frequencies 3, 7, and 5 respectively. Calculate the estimated mean using midpoints.

Answer: 54

Question 4: Describe why midpoints are important in calculating estimated means for grouped data.

Answer: Midpoints represent the center of each class interval, allowing for an approximation of data distribution when actual data points are unknown.

Question 5: In a frequency table, the class interval 15–25 has a midpoint of 20. What is the midpoint of the class interval 25–35?

Answer: 30

Question 6: Plot the graph of y=2x for x-values from 0 to 10 on the grid.

Answer: Students will draw a line passing through points (0,0), (1,2), ..., (10,20).

Question 7: Construct a triangle with base on the grid, with vertices at (2,2), (6,2), and (4,6). Show the midpoints of each side.

Answer: ["(4,2)","(3,4)","(5,4)"]

Question 8: A class interval is 70–80 with a frequency of 12. Calculate its midpoint and explain its significance in estimating the mean.

Answer: 75; it is the central value used to approximate data within the interval for the estimated mean calculation.

Question 9: A student makes a common mistake by calculating the midpoint as the average of the class limits. Identify and correct the mistake if the class interval is 35–45.

Answer: The correct midpoint is (35+45)/2=40. The mistake is assuming it is simply the average; it is actually the sum of limits divided by 2.

Question 10: Given the class intervals 10–20, 20–30, 30–40 with frequencies 4, 6, and 10 respectively, calculate the estimated mean of the data.

Answer: 26

Question 11: Explain how the use of midpoints affects the accuracy of the estimated mean in grouped data, especially when data is skewed.

Answer: Using midpoints provides an approximation that assumes data is evenly distributed within intervals; in skewed data, this can lead to inaccuracies.

Question 12: Challenge: Given the class intervals 5–15, 15–25, 25–35, 35–45 with frequencies 8, 12, 10, 6, calculate the estimated mean and explain each step.

Answer: Midpoints: 10, 20, 30, 40. Total frequency: 8+12+10+6=36. Sum of (midpoint×frequency): 10×8 + 20×12 + 30×10 + 40×6=80+240+300+240=860. Estimated mean: 860/36 ≈ 23.89. Each step involves calculating midpoints, multiplying by frequency, summing, then dividing by total frequency.