Question 1: Given the cumulative frequency table below, find the 50th percentile (median) value: | Class Interval | Cumulative Frequency | |------------------|------------------------| | 0 - 10 | 5 | | 10 - 20 | 15 | | 20 - 30 | 30 | | 30 - 40 | 45 | | 40 - 50 | 60 |

Answer: 25

Question 2: Plot the cumulative frequency curve for the data in Question 1 on the grid. Mark the point corresponding to the median.

Answer: Student plots on grid; median at cumulative frequency 30, corresponding to class 20-30.

Question 3: A dataset has the following cumulative frequencies: | Value | Cumulative Frequency | |--------|------------------------| | 5 | 10 | | 10 | 25 | | 15 | 40 | | 20 | 55 | Find the 50th percentile value.

Answer: 15

Question 4: In a survey of 200 students, the cumulative frequency for the ages is given. The 50th percentile age is found to be 16.5 years. If the cumulative frequency just before this age is 98, what is the cumulative frequency after this age?

Answer: 200

Question 5: Explain why the median is useful in understanding the data set and how it can be affected by outliers.

Answer: Median provides the middle value, less affected by extreme outliers, giving a better central tendency measure in skewed data.

Question 6: Using the cumulative frequency table below, find the median for the data: | Class Interval | Cumulative Frequency | |------------------|------------------------| | 0 - 15 | 12 | | 15 - 30 | 27 | | 30 - 45 | 43 | | 45 - 60 | 58 | | 60 - 75 | 70 |

Answer: 37.5

Question 7: Construct a cumulative frequency graph for the following data and determine the median age: Ages: 10, 12, 14, 16, 18 Frequencies: 4, 6, 8, 10, 12

Answer: Median age around the 50th percentile point, approximately 16.

Question 8: A survey records ages, with the following cumulative frequency data: | Age | Cumulative Frequency | |-----|------------------------| | 20 | 20 | | 25 | 50 | | 30 | 80 | | 35 | 100 | Identify the median age.

Answer: 25

Question 9: A class has 40 students. Their test scores have a cumulative frequency distribution with the median score at 75. The cumulative frequency just before 75 is 18. What is the total number of students?

Answer: 40

Question 10: Identify and correct the mistake: A student finds the median by taking the average of the two middle values in a data set with an odd number of entries.

Answer: Incorrect; for an odd number of data points, median is the middle value, not the average of two.

Question 11: Calculate the 50th percentile of the data: 12, 15, 14, 16, 15, 13, 17, 14.

Answer: 14.5