Question 1: Given the frequency table below, complete the cumulative frequency column: | Class Interval | Frequency | |------------------|-----------| | 10-19 | 5 | | 20-29 | 8 | | 30-39 | 12 | | 40-49 | 7 |

Answer: 5,13,25,32

Question 2: Calculate the total number of data points using the cumulative frequency table from Question 1.

Answer: 32

Question 3: Plot the cumulative frequency against the upper bounds of each class interval using the data from Question 1.

Answer: Students plot points (19,5), (29,13), (39,25), (49,32) and connect with a line.

Question 4: Explain why the cumulative frequency can never decrease as you move through the table.

Answer: Because cumulative frequency adds up total data points, it cannot decrease; it either stays the same or increases.

Question 5: A class interval has a frequency of 15 and the previous cumulative frequency is 40. What is the new cumulative frequency?

Answer: 55

Question 6: A cumulative frequency table shows 60 data points up to class 50-59. If the cumulative frequency for 60-69 is 75, how many data points are in the 60-69 class?

Answer: 15

Question 7: In a cumulative frequency table, the total frequency for all classes is 120. If the cumulative frequency at 70-79 is 95, how many data points are in the class 70-79?

Answer: 25

Question 8: A student incorrectly calculates the cumulative frequency for the class 20-29 as 20 instead of adding the previous cumulative frequency. Identify and correct the mistake in this calculation.

Answer: They should add the class frequency (which might be 8) to the previous cumulative frequency, not list it as 20 alone.

Question 9: Construct a cumulative frequency table for the following data: Frequencies of ages in a class: 5, 7, 9, 4, 6. The ages are grouped in intervals of 1 year starting from 10-14.

Answer: Construct table with class intervals 10-14, 15-19, 20-24, 25-29, 30-34 and compute cumulative frequencies accordingly.

Question 10: A cumulative frequency graph shows that at the upper boundary of 50, the cumulative frequency is 80. The total number of data points is 100. What is the approximate number of data points in the interval 51-60?

Answer: Approximately 20

Question 11: Identify a common mistake students make when constructing cumulative frequency tables and suggest a way to avoid it.

Answer: Students often forget to add each new frequency to the previous cumulative total; to avoid this, always perform running addition step-by-step.