Introduction: This is another guaranteed question on Paper II. Marks are awarded for accurate drawing and correct interpretation. Always use a pencil for graphs. The cumulative frequency curve is particularly important for finding the median and quartiles.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Define): For the class interval 20-29, what are the lower and upper class limits? What are the lower and upper class boundaries?

• Prompt 2 (Construct): Given a frequency distribution with equal class intervals, list the steps to draw a histogram.

• Prompt 3 (Construct): How do you draw a frequency polygon from a histogram?

• Prompt 4 (Construct): What values are plotted on the x-axis and y-axis to draw a cumulative frequency curve (ogive)?

• Prompt 5 (Interpret): Given the data set {5, 8, 10, 15, 20}, what is the median?

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Task): Draw a histogram for the data: | Weight (kg) | 40-45 | 45-50 | 50-55 | 55-60 | |---|---|---|---|---| | Students | 8 | 12 | 7 | 3 |

• Prompt 2 (Task): Construct a cumulative frequency table and draw the ogive for the data above.

• Prompt 3 (Interpret): From the ogive, find the median weight.

• Prompt 4 (Interpret): Find the first quartile (Q1) and the third quartile (Q3) of the weights.

• Prompt 5 (Calculate): Calculate the interquartile range (IQR) of the weights.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Task): Construct a histogram for the following data with unequal class intervals: | Time (min) | 0-10 | 10-20 | 20-40 | 40-50 | |---|---|---|---|---| | Frequency | 6 | 10 | 16 | 5 |

• Prompt 2 (Construct): Draw the frequency polygon for the data in the previous prompt without first drawing the histogram.

• Prompt 3 (Interpret): What does the interquartile range tell you about a set of data?

• Prompt 4 (Analysis): From your ogive, estimate the number of students whose weight is more than 52 kg.

• Prompt 5 (Problem Solve): For a set of 60 data points, at what position on the cumulative frequency axis would you find the median, Q1, and Q3?

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Challenge): The median of the following distribution is 24. Find the value of x. | Class | 0-10 | 10-20 | 20-30 | 30-40 | |---|---|---|---|---| | Freq. | 5 | 25 | x | 18 |

• Prompt 2 (Compare): Two basketball teams, A and B, have their player heights represented by two separate ogives. How would you use the ogives to determine which team is generally taller? How would you determine which team's heights are more consistent (less spread out)?

• Prompt 3 (Derive): A frequency polygon and a histogram are drawn for the same data. Prove that the area of the frequency polygon is equal to the area of the histogram.

• Prompt 4 (Analysis): For the data in the "B" level prompt 1, if the top 20% of the times are considered "long", what is the minimum time for a long duration? (Use the ogive).

• Prompt 5 (Synthesis): Explain the relationship between the slope of the cumulative frequency curve and the frequency density of the distribution. Where is the curve steepest, and what does this signify?