Question 1: Calculate the midpoints of the following class intervals: 10-20, 20-30, 30-40.

Answer: 15, 25, 35

Question 2: Plot the midpoints for the class intervals 0-5, 5-10, 10-15 on the grid.

Answer:

Question 3: Given class intervals 40-50, 50-60, 60-70 with frequencies 12, 20, 15, calculate their midpoints and prepare to plot.

Answer: 45, 55, 65

Question 4: Explain why midpoints are used in constructing frequency polygons instead of class boundaries.

Answer: Midpoints provide a representative value for each class interval, making the frequency polygon a better visual approximation of the data distribution.

Question 5: Construct a frequency polygon by plotting midpoints for class intervals 15-25, 25-35, 35-45 with frequencies 8, 14, 10.

Answer:

Question 6: A set of class intervals 5-10, 10-15, 15-20 has midpoints 7.5, 12.5, 17.5. If the frequencies are 6, 9, 4, plot the points and draw the frequency polygon.

Answer:

Question 7: A histogram shows class intervals with midpoints and frequencies: 10-20 (15, 12), 20-30 (25, 18). Calculate midpoints and explain how they relate to the frequency polygon.

Answer: Midpoints are 15 and 25. They serve as the x-coordinates for plotting the frequency polygon, linking the histogram to the polygon.

Question 8: Given class intervals 0-10, 10-20, 20-30 with frequencies 5, 10, 15, find midpoints and identify any errors if plotted incorrectly as 5, 15, 25.

Answer: Midpoints are 5, 15, 25. The error is plotting the midpoint of 0-10 as 5 instead of 5, which is correct; however, if plotted at 0 and 10 instead, that would be incorrect.

Question 9: Plot the midpoints for class intervals 12-18, 18-24, 24-30 and connect the points to form a frequency polygon.

Answer:

Question 10: Explain how errors in calculating midpoints can affect the shape of a frequency polygon.

Answer: Incorrect midpoints distort the position of data points, leading to a misrepresentation of the data's distribution and potentially misleading conclusions.

Question 11: Identify and correct the mistake: Given class intervals 25-35, 35-45 with midpoints incorrectly calculated as 30, 45.

Answer: The midpoints should be 30 and 40; 45 is incorrect for 35-45.

Question 12: Using the grid, plot the midpoints of class intervals 0-8, 8-16, 16-24 and their respective frequencies 4, 7, 3. Connect the points to complete the frequency polygon.

Answer: