Question 1: Calculate the midpoint between the class boundaries 10-20 and 20-30.

Answer: 15

Question 2: Find the midpoint of the values 35 and 45.

Answer: 40

Question 3: Plot the midpoint between 50 and 60 on the grid.

Answer: 55

Question 4: Calculate the midpoint between the class boundaries 70-80 and 80-90.

Answer: 75

Question 5: In a grouped frequency distribution, the lower boundaries are 0, 10, 20, 30. Find the midpoints to plot for these classes.

Answer: 5, 15, 25

Question 6: Explain why midpoints are important when constructing a frequency polygon.

Answer: Midpoints represent the center of each class interval, allowing the data to be plotted smoothly and accurately in a frequency polygon.

Question 7: Given the class boundaries 15-25, 25-35, 35-45, find their midpoints and describe how these help in plotting the frequency polygon.

Answer: Midpoints are 20, 30, 40. They are plotted on the x-axis to connect the frequency data points smoothly.

Question 8: Construct a frequency polygon given the midpoints 10, 20, 30, 40 and corresponding frequencies 5, 8, 6, 4. Show all steps.

Answer: Plot points at (10,5), (20,8), (30,6), (40,4), then connect with straight lines.

Question 9: A data set has class boundaries: 0-10, 10-20, 20-30, with frequencies 3, 7, 5. Calculate the midpoints and explain their use in plotting the frequency polygon.

Answer: Midpoints are 5, 15, 25. They are used as x-coordinates to plot the frequency data points for the polygon.

Question 10: Identify the common mistake students make when calculating midpoints and suggest how to correct it.

Answer: Adding the boundaries instead of averaging them. Correct by dividing the sum of boundaries by 2.

Question 11: Plot the midpoints for the class boundaries 60-70 and 70-80, then connect the points to form part of a frequency polygon.

Answer: Midpoints are 65 and 75; plot these points and connect with a straight line.