Question 1: Calculate the estimated mean for the grouped data: Class intervals: 0-10, 10-20, 20-30. Frequencies: 5, 8, 7. Use the midpoints for calculations.

Answer: 17

Question 2: Using the data: Class widths of 5, Frequencies: 3, 6, 9, 12. Calculate Σfx and Σf to find the estimated mean.

Answer: Σfx=147, Σf=30, mean=4.9

Question 3: A grouped frequency table shows class intervals: 40-50, 50-60, 60-70, 70-80 with frequencies 4, 9, 6, 1. Calculate the estimated mean.

Answer: 55

Question 4: Identify the error in this calculation: The class midpoints were taken as 5, 15, 25, with frequencies 2, 3, 4. Σfx was calculated as 80, and Σf as 9, leading to a mean of 8.9.

Answer: Incorrect midpoints; actual midpoints should be 7.5, 17.5, 27.5.

Question 5: Calculate the estimated mean for the data: Class intervals: 0-20, 20-40, 40-60. Frequencies: 10, 15, 5.

Answer: 33.33

Question 6: Plot the graph of y=2x for the range x=0 to 10 on the grid. (Students draw on the grid.)

Answer: Graph plotted accordingly.

Question 7: Construct a histogram with class intervals: 0-5, 5-10, 10-15, 15-20, and frequencies: 3, 7, 5, 2. Label the axes clearly.

Answer: Histogram constructed with correct bars.

Question 8: Calculate the estimated mean for data with class intervals 0-25, 25-50, 50-75, with frequencies 4, 6, 10. Use midpoints to find the mean.

Answer: 50

Question 9: A student calculates the mean as Σfx/Σf but forgets to use the midpoints for the class intervals. What mistake have they made?

Answer: They used class boundaries or frequencies instead of midpoints, leading to an incorrect estimate.

Question 10: Given the data: Class intervals: 0-10, 10-20, 20-30, 30-40. Frequencies: 2, 4, 6, 8. Find Σfx and Σf and then calculate the estimated mean.

Answer: Σfx=140, Σf=20, mean=7

Question 11: Explain why it is important to use the midpoints of class intervals when calculating the estimated mean.

Answer: Midpoints provide a representative value for each class, leading to a more accurate estimate.

Question 12: Identify and correct the common mistake in calculating Σfx when students forget to multiply class midpoints by frequencies.

Answer: Students only summed frequencies or class boundaries, missing the multiplication by midpoints, resulting in incorrect Σfx.