Final answer:
The cumulative frequency for scores of 20 or lower is the sum of the frequencies in the intervals up to 20. The relative cumulative frequency is this cumulative frequency divided by the total number of quiz participants.
Step-by-step explanation:
To calculate the cumulative frequency and the relative cumulative frequency from a histogram is to compile and analyze the frequency of data up to a certain point. Based on the intervals provided (1-5, 6-10, 11-15, 16-20, 21-25, 26-30, 31-35, and 36-40), we would look at the histogram and count the number of quiz scores in each interval, then sum these values up to the 20 or lower interval.
The cumulative frequency for students who earned a score of 20 or lower is the sum of the frequencies for the intervals 1-5, 6-10, 11-15, and 16-20. To find the relative cumulative frequency, take the cumulative frequency and divide it by the total number of students. This gives us the proportion of students earning a score of 20 or less.
For example, let's say there are 5 students in the 1-5 range, 10 in the 6-10 range, 8 in the 11-15 range, and 4 in the 16-20 range. The total number of students who scored 20 or lower is 5+10+8+4 = 27. If there are 35 students in total, the relative cumulative frequency would be 27/35 which can be expressed as a decimal or a percentage.