Question 1: Calculate the modal class for the following grouped frequency data: Class intervals: 0-10, 10-20, 20-30, 30-40, 40-50 Frequencies: 5, 12, 18, 10, 4

Answer: 20-30

Question 2: Explain why choosing the highest frequency alone might lead to a common misconception about the modal class.

Answer: Students might think the modal class is always the one with the highest frequency, but it depends on the grouped data and the class intervals chosen.

Question 3: Identify the mistake in the following calculation: The frequency for 20-30 is 18, and for 30-40 is 10. The student states the modal class is 30-40 because it has a high frequency.

Answer: They should identify 20-30 as the modal class, not 30-40, because 20-30 has the highest frequency.

Question 4: A grouped data table shows class intervals 0-5, 5-10, 10-15, 15-20 with frequencies 3, 7, 12, 9. What is the modal class? Show your working.

Answer: 10-15

Question 5: In a frequency distribution, the classes are overlapping or not mutually exclusive. How does this affect the determination of the modal class?

Answer: Overlapping classes can cause confusion in identifying the modal class because the highest frequency might belong to overlapping intervals, making it ambiguous.

Question 6: Given a grouped frequency table, students incorrectly identify the modal class because they ignore the class widths. Correct the mistake and explain.

Answer: They need to consider the class widths because a class with a higher frequency but larger width might not be the true modal class; the modal class is the one with the highest modal frequency considering class widths.

Question 7: A teacher shows a histogram where the tallest bar is for the class 20-30. However, the frequency for 30-40 is higher when counts are summed across sub-intervals. What common misconception does this illustrate?

Answer: Students might rely solely on visual cues like bar height without considering actual frequency counts or class overlaps.

Question 8: Construct a frequency table with class intervals 0-10, 10-20, 20-30, 30-40, 40-50, where the modal class is 20-30. Provide the frequencies and justify your choice.

Answer: Possible frequencies: 4, 7, 15, 8, 3. Justification: 20-30 has the highest frequency of 15.

Question 9: A student incorrectly states that the median class must be the same as the modal class in grouped data. Is this always true? Explain your reasoning.

Answer: No, the median class is the class containing the median value, which may differ from the modal class if the data are skewed or have multiple modes.

Question 10: For the grouped data: 0-10 (5), 10-20 (12), 20-30 (18), 30-40 (10), 40-50 (4). If a new student mistakenly believes the modal class is 10-20 because it is the second highest frequency, what is the correction?

Answer: The modal class is 20-30, as it has the highest frequency (18).

Question 11: Calculate the approximate mode of a grouped data distribution with the following peak: class interval 20-30, frequency 18; the previous class 10-20, frequency 12; the next class 30-40, frequency 10. Use the modal formula.

Answer: Mode ≈ L + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h = 20 + [(18 - 12) / (2×18 - 12 - 10)] × 10 = 20 + (6 / 14) × 10 ≈ 23.43