Question 1: Given a cumulative frequency table, find the value of Q1.

Answer: Calculate position = (N+1)/4, then find the corresponding value.

Question 2: Determine the median (Q2) for the data set using the cumulative frequency table.

Answer: Calculate position = (N+1)/2, then identify the value.

Question 3: Find Q3 using the cumulative frequency data provided.

Answer: Calculate position = 3(N+1)/4, then find the corresponding value.

Question 4: Construct a cumulative frequency table for the data: 5, 7, 8, 10, 12, 15, 18.

Answer: Create cumulative totals and mark class boundaries accordingly.

Question 5: A data set has 50 values with Q1 at the 12.5th position. What is the value of Q1?

Answer: Position is between 12th and 13th data points; interpolate if needed.

Question 6: Explain why Q2 is also known as the median.

Answer: Q2 divides the data set into two equal halves.

Question 7: In a cumulative frequency table, Q3 is at the 75th percentile. How do you locate its value?

Answer: Calculate position = 3(N+1)/4, then interpolate if necessary.

Question 8: A histogram shows data grouped in intervals. How can you estimate the quartiles from this graph?

Answer: Identify cumulative frequencies at relevant quartile positions.

Question 9: Calculate Q1, Q2, and Q3 for the following cumulative frequencies: 10, 20, 30, 40, 50.

Answer: Q1 at 25th percentile, Q2 at 50th, Q3 at 75th; interpolate as needed.

Question 10: Identify a common mistake when calculating Q1 and explain how to avoid it.

Answer: Incorrectly calculating the position; always use (N+1)/4 and interpolate carefully.

Question 11: A data set is skewed. How might this affect your calculation of quartiles?

Answer: Skewness can cause quartiles to be closer or further apart; interpret with caution.

Question 12: Given the cumulative frequency data, find the interquartile range (IQR).

Answer: IQR = Q3 - Q1; calculate each and subtract.