Question 1: Given the frequency table below, find the median class and the median value. | Class Interval | Frequency | |------------------|-----------| | 10 - 20 | 5 | | 20 - 30 | 8 | | 30 - 40 | 12 | | 40 - 50 | 7 | | 50 - 60 | 3 |

Answer: 30 - 40; median = 30 + [(24 - 13) / 12] * 10 = 33.33

Question 2: Calculate the median value for the following frequency table: | Class | Frequency | |--------|------------| | 0-5 | 4 | | 5-10 | 9 | | 10-15 | 6 | | 15-20 | 11 |

Answer: 10-15; Median = 10 + [(15 - 9) / 11] * 5 = 12.27

Question 3: A frequency table shows the ages of students: | Age Range | Number of Students | |-------------|---------------------| | 10-15 | 6 | | 15-20 | 10 | | 20-25 | 8 | | 25-30 | 4 | Find the median age.

Answer: 15-20; median = 15 + [(14 - 6) / 10] * 5 = 17

Question 4: A frequency table has an error in the cumulative total. Explain what mistake students might make when calculating the median and how to correct it.

Answer: Students may incorrectly sum frequencies or assume the total is 20 instead of 24; they should sum all frequencies correctly and find the class where the median position lies.

Question 1: A class recorded the number of books read by students over a month. The frequency table is: | Number of Books | Frequency | |------------------|-----------| | 0-2 | 4 | | 3-5 | 10 | | 6-8 | 7 | | 9-11 | 3 | Find the median number of books read and explain which class contains the median.

Answer: Median class = 3-5; median number ≈ 4.4 books (using cumulative frequency and median formula).

Question 2: A survey of 50 people recorded their daily screen time in hours. The frequency table is: | Hours | Frequency | |--------|-----------| | 0-2 | 8 | | 3-5 | 15 | | 6-8 | 20 | | 9-11 | 7 | Calculate the median screen time and justify your answer.

Answer: Median class = 6-8 hours; median ≈ 6 + [(25 - 23) / 20] * 2 = 6.2 hours.

Question 3: Explain why choosing the incorrect median class can lead to inaccuracies in median calculations, and how to avoid this mistake.

Answer: Choosing the wrong median class results from misreading cumulative frequencies; students should carefully identify where the median position falls in the cumulative frequency.

Question 4: A frequency table lists the scores of students in an exam: | Score Range | Frequency | |--------------|-----------| | 0-20 | 5 | | 20-40 | 15 | | 40-60 | 20 | | 60-80 | 10 | Determine the median score range and discuss a common mistake students might make in this calculation.

Answer: Median range = 40-60; students might incorrectly identify the class or miscalculate the cumulative total.

Question 1: A company records the number of hours employees work weekly. The frequency table is: | Hours per week | Number of employees | |------------------|---------------------| | 30-35 | 8 | | 36-40 | 15 | | 41-45 | 12 | | 46-50 | 5 | Find the median weekly hours and explain the significance of the median in this context.

Answer: Median class = 36-40 hours; median ≈ 38.75 hours; median indicates typical work hours.

Question 2: In a health survey, the number of steps walked daily is categorized: | Steps | Number of people | |--------|------------------| | 0-3000 | 6 | | 3001-6000 | 14 | | 6001-9000 | 18 | | 9001-12000 | 12 | Determine the median number of steps and discuss any misconceptions students might have when interpreting the median from this data.

Answer: Median class = 6001-9000; median ≈ 6625 steps; misconception may include misreading cumulative frequency or assuming the wrong class.

Question 1: Given a frequency table with uneven class widths: | Class Interval | Frequency | |------------------|-----------| | 0-5 | 3 | | 6-15 | 7 | | 16-25 | 12 | | 26-35 | 8 | Explain how the unequal class widths affect the calculation of the median and how to adjust your method accordingly.

Answer: Unequal class widths mean simple interpolation may be inaccurate; students should convert to midpoints and calculate median based on weighted data.

Question 2: Design a frequency table where the median calculation would be intentionally misleading if students assume all classes are equal. Describe the features of this table.

Answer: Use classes with highly unequal widths and uneven frequencies; students might incorrectly interpolate median assuming equal class sizes.

Question 1: True or False: The median is always the middle data point when data is ordered. Explain your answer.

Answer: False; median is the middle value in a grouped data set, which may not be an actual data point.

Question 2: Plot the graph of y=2x for x values between 0 and 10 on the grid. Identify the median point of the plotted line within the interval.

Answer: Median at x=5; y=10.

Question 3: Construct a triangle with sides of lengths 3, 4, and 5 on the grid. Determine the median length from the right angle to the hypotenuse.

Answer: Median length = 2.5 units.