Question 1: A histogram displays the following data: Class intervals 10-15, 15-25, 25-40, with frequencies 12, 24, and 18 respectively. Calculate the frequency density for each class interval.

Answer: 10-15: 12/5=2.4; 15-25: 24/10=2.4; 25-40: 18/15=1.2

Question 2: The class intervals 5-10, 10-20, 20-35 have frequencies 8, 16, 14 respectively. Calculate the frequency densities and identify which class has the highest density.

Answer: 5-10: 8/5=1.6; 10-20: 16/10=1.6; 20-35: 14/15≈0.93. The highest density is 1.6, shared by 5-10 and 10-20.

Question 3: A histogram shows data for class intervals 0-8, 8-20, 20-50 with frequencies 10, 15, 20. Calculate the frequency densities and determine which class has the smallest density.

Answer: 0-8: 10/8=1.25; 8-20: 15/12=1.25; 20-50: 20/30≈0.67. Smallest density: 20-50.

Question 4: A histogram has class intervals 0-4, 4-9, 9-15 with frequencies 5, 10, 15 respectively. Calculate the frequency densities and explain which class has the highest density and why.

Answer: 0-4: 5/4=1.25; 4-9: 10/5=2; 9-15: 15/6=2.5. The class 9-15 has the highest density because it has the largest frequency per unit class width.

Question 5: Construct a histogram with class intervals 0-3, 3-8, 8-20, and corresponding frequencies 9, 21, 30. Calculate the frequency densities and plot the histogram on the grid provided.

Answer: 0-3: 9/3=3; 3-8: 21/5=4.2; 8-20: 30/12=2.5. Students will plot bars with heights proportional to these densities.

Question 6: A data set is represented with class intervals 10-20, 20-35, 35-50, with frequencies 20, 25, 15. Find the frequency densities and identify the class with the most uniform distribution of data.

Answer: 10-20: 20/10=2; 20-35: 25/15≈1.67; 35-50: 15/15=1. The class 35-50 has the most uniform distribution as it has the lowest variation in density.

Question 7: A histogram has class intervals 0-6, 6-12, 12-24 with frequencies 18, 24, 12. Calculate the frequency densities and determine if the histogram suggests uniform or varying data density.

Answer: 0-6: 3; 6-12: 2; 12-24: 0.5. Varying densities indicate non-uniform data distribution.

Question 8: In a histogram, the class interval 20-60 has a frequency of 40. If the frequency density is 0.8, what is the class width? Show your calculations.

Answer: Width = Frequency / Density = 40 / 0.8 = 50 units.

Question 9: A histogram displays class intervals 0-10, 10-25, 25-50, with frequency densities 1.2, 1.0, 0.6 respectively. Calculate the corresponding frequencies for each class interval.

Answer: 0-10: 1.2×10=12; 10-25: 1.0×15=15; 25-50: 0.6×25=15.

Question 10: Identify and correct the mistake: A student calculates the frequency density for a class 5-15 with frequency 20 as 20/10=2. Is this correct? Explain your reasoning.

Answer: Yes, because the class width is 15-5=10, so frequency density = 20/10=2. The calculation is correct.