Question 1: Given the frequency table below, identify the mode and its highest frequency. | Data Value | Frequency | |--------------|------------| | 12 | 5 | | 15 | 8 | | 18 | 3 | | 20 | 8 | | 22 | 2 |

Answer: 15 and 20, highest frequency 8

Question 2: Calculate the mode from the following frequency data: | Number | Frequency | |---------|------------| | 7 | 4 | | 9 | 6 | | 11 | 6 | | 13 | 3 |

Answer: 9 and 11, highest frequency 6

Question 3: A class recorded the number of books read in a month. The frequency table is: | Books | Frequency | |--------|------------| | 2 | 3 | | 3 | 7 | | 4 | 5 | | 5 | 7 | | 6 | 2 | Identify the mode(s) and explain what it tells you about the data.

Answer: Modes are 3 and 5, both with highest frequency 7; this shows these are the most common number of books read.

Question 4: Construct a frequency table with data values 10, 12, 14, 16, and 18, where the highest frequency is 4. Assign suitable frequencies to illustrate the highest frequency.

Answer: Any data values with frequency 4, e.g., 10 (4), 12 (3), 14 (2), 16 (2), 18 (2)

Question 5: In a survey, the number of pets owned by students is summarized: | Pets | Frequency | |-------|------------| | 0 | 5 | | 1 | 12 | | 2 | 15 | | 3 | 10 | | 4 | 8 | What is the mode, and how many students own that number of pets?

Answer: 2 pets, 15 students

Question 6: A teacher recorded the number of students arriving late each day over a week: | Day | Late Arrivals | |-------|--------------| | Monday | 3 | | Tuesday | 2 | | Wednesday | 4 | | Thursday | 3 | | Friday | 2 | Determine the mode of late arrivals and explain its significance.

Answer: Late arrivals mode are 2 and 3, both with frequency 2; this indicates the most common number of late students.

Question 7: The frequency table shows: | Score | Frequency | |--------|------------| | 50 | 3 | | 60 | 7 | | 70 | 7 | | 80 | 2 | Identify the mode(s) and discuss what this indicates about the scores.

Answer: Scores 60 and 70, both with highest frequency 7; most students scored in this range.

Question 8: A data set has the following frequency distribution: | Category | Frequency | |---------|------------| | A | 2 | | B | 4 | | C | 2 | | D | 2 | What is the mode, and what mistake might students make when identifying it?

Answer: Mode is B with frequency 4; common mistake is selecting multiple modes without proper analysis.

Question 9: Use the following frequency table to find the data value(s) with the highest frequency: | Category | Frequency | |------------|------------| | 100 | 2 | | 110 | 5 | | 120 | 5 | | 130 | 3 |

Answer: 110 and 120, highest frequency 5

Question 10: Explain why a frequency table with two data values sharing the highest frequency is considered bimodal. Provide an example based on a real-world scenario.

Answer: When two data values have the same highest frequency, the dataset is bimodal, indicating two most common outcomes, e.g., most common shoe sizes being 8 and 9 in a class.

Question 11: Identify and correct the mistake: A student finds the mode of a dataset as 10, but the frequency table shows 10 occurs only once. What error did they make?

Answer: The student incorrectly identified 10 as the mode; the error is assuming the most frequent data point is the mode when it actually occurs only once.