Question 1: A histogram shows the number of students in different height ranges. The class intervals are 140-150 cm, 150-165 cm, and 165-180 cm. The corresponding frequencies are 12, 24, and 18. Calculate the frequency density for each class.

Answer: 140-150 cm: 12/10=1.2; 150-165 cm: 24/15=1.6; 165-180 cm: 18/15=1.2

Question 2: Construct a histogram bar for the height range 150-165 cm with the height of 1.6 units (based on frequency density). The class width is 15 cm.

Answer: Draw a bar with height 1.6 over the interval 150-165 cm, width 15 cm.

Question 3: A dataset has class intervals 0-5, 5-15, and 15-25 with frequencies 10, 40, and 50. Calculate the frequency density for each class.

Answer: 0-5: 10/5=2; 5-15: 40/10=4; 15-25: 50/10=5

Question 4: Plot the histogram given the class intervals and frequency densities: 20-30 (2.5), 30-50 (4), 50-70 (3).

Answer: Draw bars over each interval with heights 2.5, 4, and 3 respectively, widths corresponding to class widths.

Question 5: A histogram's class intervals are 10-20, 20-40, and 40-70 with frequencies 15, 30, and 35. Which class has the highest frequency density?

Answer: 10-20: 15/10=1.5; 20-40: 30/20=1.5; 40-70: 35/30≈1.17; both 10-20 and 20-40 have highest density (1.5).

Question 6: Explain why the class 40-70 has a lower frequency density than the class 20-40 in the previous question, despite having a higher frequency.

Answer: Because the class width of 40-70 (30) is larger than 20-40 (20), leading to a lower frequency density despite the higher frequency.

Question 7: A histogram shows the number of hours spent on a task with class intervals of 0-2, 2-4, 4-8, and 8-12 hours. The frequencies are 5, 15, 25, and 20. Calculate the frequency densities for each interval.

Answer: 0-2: 5/2=2.5; 2-4: 15/2=7.5; 4-8: 25/4=6.25; 8-12: 20/4=5

Question 8: Construct a histogram bar for the class interval 4-8 hours with a height of 6.25 units.

Answer: Draw a bar with height 6.25 over 4-8 hours, width 4 hours.

Question 9: A survey shows data with class intervals 0-10, 10-20, 20-40, with frequencies 8, 16, and 24. Calculate the frequency density for the 20-40 interval.

Answer: 20-40: 24/20=1.2

Question 10: Identify a common mistake made when calculating frequency density with unequal class widths and describe how to avoid it.

Answer: A common mistake is dividing frequency by the total class width without considering the actual interval difference each class covers; always use the exact class width for each interval.

Question 11: A histogram displays data with class widths of 5, 10, and 15. The frequencies are 25, 50, and 75 respectively. Which class has the highest frequency density?

Answer: Class with width 5: density=25/5=5; 10: 50/10=5; 15: 75/15=5; all have equal density (5).