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, and 20-30.

Answer: 5, 15, 25

Question 3: A grouped frequency table shows ages of students in a class. The class intervals are 10-20, 20-30, and 30-40. Calculate the midpoints for each class.

Answer: 15, 25, 35

Question 4: In a histogram, the class interval 40-50 has a midpoint of 45. What is the lower boundary of this class?

Answer: 42.5

Question 5: Estimate the mean height of a group of people using midpoints of the class intervals: 150-160, 160-170, 170-180. The frequencies are 5, 8, and 7 respectively.

Answer: 168

Question 6: A survey records income in brackets: 0-1000, 1000-2000, 2000-3000. If the midpoints are used to estimate average income, and the frequencies are 10, 15, and 5, what is the estimated mean income?

Answer: 1666.67

Question 7: Explain why using midpoints of class intervals is useful when estimating the mean of grouped data.

Answer: Midpoints simplify calculations by representing each class interval with a single value, making it easier to estimate the overall mean without needing individual data points.

Question 8: A class interval is incorrectly labeled as 25-35, but the actual lower boundary is 24.5. What is the correct midpoint?

Answer: 29.25

Question 9: A grouped data table shows class intervals and frequencies. The class intervals are 50-60, 60-70, 70-80, and the corresponding midpoints are 55, 65, 75. If the total frequency is 30 and the sum of (midpoints × frequencies) is 1800, what is the estimated mean?

Answer: 60

Question 10: Identify and correct the error in this calculation of the midpoint of the interval 10-20: the student calculated (10+20)/3.

Answer: The correct calculation is (10+20)/2 = 15.

Question 11: Construct a diagram on the grid to represent the class intervals 0-10, 10-20, 20-30 with their midpoints marked. (No answer; student draws on grid.)

Answer: