Question 1: Given the frequency table below, determine the mode and explain if it's correct. | Data Value | Frequency | |--------------|-----------| | 5 | 8 | | 7 | 12 | | 9 | 12 | | 11 | 5 |

Answer: The modes are 7 and 9 because both have highest frequency 12.

Question 2: A student claims the mode is 7 because it appears most often in the data. Identify and correct the misconception.

Answer: The misconception is that the mode is 7 based on its frequency alone. Since 9 also appears 12 times, both 7 and 9 are modes, so the data is bimodal.

Question 3: Construct a frequency table where the highest frequency is 15. Show at least 4 data values.

Answer: Data values: 3, 5, 7, 9 with frequency 15 each.

Question 4: A table shows the following frequencies: 4, 10, 10, 6. What is the highest frequency? Is the mode unique? Explain.

Answer: The highest frequency is 10. The mode is not unique; both values with frequency 10 are modes.

Question 5: Identify a common mistake students make when finding the mode from a frequency table and explain how to avoid it.

Answer: A common mistake is selecting a value with the highest data point rather than the highest frequency. To avoid this, always compare frequencies to identify the mode.

Question 6: Plot the following frequency data on the grid: Data values 1-5 with frequencies 2, 4, 5, 4, 2. Identify the mode visually on your plot.

Answer: The mode is at data value 3, which has the highest frequency of 5.

Question 7: A frequency table shows a highest frequency of 7 for the data value 12. Another student claims the mode is 12. Is this correct? Why or why not?

Answer: Yes, if 12 has the highest frequency of 7, then 12 is the mode. The student is correct.

Question 8: Given the data: 3, 3, 4, 4, 4, 5. Construct a frequency table and determine the mode, explaining your reasoning.

Answer: Frequency table: 3 appears 2 times, 4 appears 3 times, 5 appears 1 time. The mode is 4 because it has the highest frequency.

Question 9: A data set has multiple modes. Describe how this affects the interpretation of the mode and how to communicate this in your analysis.

Answer: Multiple modes mean the data is bimodal or multimodal. When reporting, list all modes and state that the data has more than one most frequent value.

Question 10: Identify and correct the mistake in the following student solution: Frequency table: 2(3), 4(5), 5(5), 7(4). Student states the mode is 4 because it appears most often.

Answer: The mistake is that both 4 and 5 appear 5 times, so the data is bimodal. The correct modes are 4 and 5.

Question 11: Challenge: Create a frequency table with three modes. Explain how the highest frequency relates to these modes.

Answer: Example: Data values 1, 3, 5 with frequencies 4, 4, 4. The highest frequency is 4, and all three data values are modes because they share this highest frequency.