Question 1: A histogram shows the number of students in different height ranges. The height intervals are 140-149 cm, 150-159 cm, 160-169 cm, 170-179 cm, and 180-189 cm. The corresponding frequencies are 8, 12, 15, 9, and 6. Calculate the total number of students represented in the histogram.

Answer: 50

Question 2: The histogram shows frequencies for different age groups. If the frequency for the 20-29 age group was mistakenly recorded as 24 instead of 14, what would be the correct total number of people?

Answer: 40

Question 3: Construct a histogram with the following data: Frequency of 5 for 10-19, 12 for 20-29, 9 for 30-39, and 4 for 40-49. Use a scale where 1 unit on the grid equals 1 student.

Answer: Students should draw bars with heights corresponding to the frequencies, starting at 10 for 10-19, 12 for 20-29, etc.

Question 4: A histogram shows class intervals and frequencies. If the interval 50-59 cm has a frequency of 10, and the total frequency is 60, what is the combined frequency of the other intervals?

Answer: 50

Question 5: A histogram displays data on daily temperatures with intervals and frequencies. The interval 10-19°C has a frequency of 15. The total number of days recorded is 75. If the other intervals sum to 45, what is the frequency for 10-19°C?

Answer: 15

Question 6: In a histogram representing monthly rainfall, the interval 20-29 mm has a frequency of 20. If the total frequency is 100, what is the combined frequency of all other intervals?

Answer: 80

Question 7: Identify and correct the mistake in this frequency calculation: The total frequency is calculated as 8 + 12 + 14 + 9 + 6 = 49, but the sum is given as 50. What is the error?

Answer: Adding 14 instead of 15; the sum should be 50 if 15 is used instead of 14.

Question 8: A student incorrectly sums the heights' midpoints times their frequencies to find the total height. Explain why this approach is incorrect for finding total frequency.

Answer: Because summing midpoints times frequencies gives the total height sum, not total frequency; total frequency is the sum of individual frequencies, not weighted sums.

Question 9: Given a histogram with intervals of 0-9, 10-19, 20-29, and 30-39, and frequencies of 4, 10, 6, and 8 respectively, find the total frequency.

Answer: 28

Question 10: A histogram shows a frequency of 7 for 50-59, 13 for 60-69, 9 for 70-79, and 5 for 80-89. Which interval has the highest frequency and what is it?

Answer: 60-69 with a frequency of 13

Question 11: Explain a common misconception when calculating total frequencies from a histogram and how to avoid it.

Answer: Students often add class midpoints instead of the actual frequencies. To avoid this, only sum the frequency values given by the height of the bars, not the midpoints.