Question 1: A student constructs a cumulative frequency table but makes an error in calculating the cumulative totals. Given the class frequencies: 5, 7, 8, 10, 6, identify the mistake in the table if the cumulative totals are listed as 5, 12, 19, 29, 31.

Answer: Incorrect cumulative total for last class; should be 36

Question 2: Calculate the correct cumulative frequency for the third class if the class frequency is 8 and the second cumulative total is 12.

Answer: 20

Question 3: A student mistakenly adds the cumulative totals instead of summing class frequencies when building the table. What is the misconception here?

Answer: Confusing cumulative totals with sum of class frequencies

Question 4: Construct a cumulative frequency table for the following class frequencies: 3, 6, 9, 12, 15. Then, identify the common mistake students make when summing these totals.

Answer: Students often forget to add the previous cumulative total when calculating subsequent totals.

Question 5: Given the data: Class frequencies = 4, 8, 12, 16, 20. A student calculates cumulative totals as 4, 8, 12, 16, 20. What is the error, and how should it be corrected?

Answer: They did not add previous totals; correct cumulative totals are 4, 12, 24, 40, 60

Question 6: In a cumulative frequency table, the total number of data points is 50. If the last cumulative total is 45, what mistake has been made?

Answer: The cumulative total is incorrect; it should be 50, indicating some data points are missing or miscounted.

Question 7: A class frequency of 10 is mistakenly not included in the cumulative total. Explain how this impacts the interpretation of the data.

Answer: The total count will be underestimated, leading to incorrect analysis of data distribution.

Question 8: A student builds a cumulative frequency table and then plots the graph. They connect data points directly without ensuring the correct scale. What common misconception does this illustrate?

Answer: Assuming the plotted points are accurate without verifying the scale or data accuracy.

Question 9: Solve the following: Given a cumulative frequency table with total of 70, and class frequencies of 7, 14, 21, 28, identify the mistake if the last cumulative total is listed as 65.

Answer: The last total is incorrect; it should be 70, not 65.

Question 10: Challenge: A student claims that cumulative frequency tables can only be built from raw data, not from grouped data. Is this true? Explain briefly.

Answer: No, cumulative frequency tables can be built from grouped data as well, but care must be taken to accurately sum group frequencies.

Question 11: Identify and correct the error in this cumulative frequency table: Class intervals are 0-10, 10-20, 20-30, with class frequencies 5, 10, 8, but the cumulative totals are 5, 15, 22.

Answer: The cumulative totals are correct; no mistake here. This is a trap to test understanding.