Question 1: Given the cumulative frequency table below, calculate Q1.

Answer: 20

Question 2: Calculate the median (Q2) for the given data in the cumulative frequency table.

Answer: 35

Question 3: Determine Q3 from the following cumulative frequency data.

Answer: 50

Question 4: Plot the cumulative frequency data on the graph paper provided, then identify the approximate values of Q1, Q2, and Q3.

Answer: Students will plot and estimate

Question 5: A dataset has a median (Q2) at 25. The lower quartile (Q1) is at 10 and the upper quartile (Q3) at 40. Explain what this suggests about the distribution of the data.

Answer: The data is skewed towards higher values since Q3 is much larger than Q2, and most data points are clustered below Q3.

Question 6: In a cumulative frequency table, Q1 is at position 15, Q2 at 30, and Q3 at 45 in the ordered data set. How many data points are there in total?

Answer: 45

Question 7: A teacher records students' test scores. The cumulative frequency shows Q1 at 22, Q2 at 45, and Q3 at 75. What percentage of students scored below Q3?

Answer: 75%

Question 8: Identify and correct the mistake in the following statement: 'Q1 is always at 25% of the data, Q2 at 50%, and Q3 at 75%.'

Answer: Quartiles indicate data points at specific data positions, not fixed percentages like percentiles.

Question 9: Using the cumulative frequency table, find the interquartile range (IQR) and interpret its meaning in the context of the data.

Answer: IQR = Q3 - Q1; indicates the spread of the middle 50% of data.

Question 10: Construct a box plot using the Q1, Q2, and Q3 values obtained from the data and describe what it reveals about the data distribution.

Answer: Students will draw and analyze the box plot for skewness and spread.

Question 11: In a data set, Q1 is at 12, Q2 at 20, and Q3 at 28. A new data point of 50 is added. Will this affect Q3? Justify your answer.

Answer: Yes, adding 50 increases Q3, as it extends the upper range of the data.