Question

Calculate cumulative and relative cumulative frequency from a histogram. The following histogram represents quiz scores and uses the interval bins: 1-5, 6-10, 11-15, 16-20, 21-25, 26-30, 31-35, and 36-40. For students who earned a score of 20 or lower on the quiz, the cumulative frequency is:

A) 8
B) 12
C) 18
D) 24

Answer 1

To calculate the cumulative frequency from a histogram, add up the frequencies for each interval. The cumulative frequency for scores of 20 or lower is 63. The relative cumulative frequency can be found by dividing the cumulative frequency by the total number of scores, which is 0.6495 (rounded to four decimal places).

Step-by-step explanation:

To calculate the cumulative frequency from a histogram, you need to add up the frequencies for each interval starting from the lowest interval. In this case, if we want to find the cumulative frequency for scores of 20 or lower, we need to add up the frequencies for all intervals up to and including the 16-20 interval. From the given histogram, the frequencies for the intervals 1-5, 6-10, 11-15, and 16-20 are 13, 15, 17, and 18 respectively. Therefore, the cumulative frequency for scores of 20 or lower is 13 + 15 + 17 + 18 = 63.

The relative cumulative frequency can be calculated by dividing the cumulative frequency for each interval by the total number of scores. In this case, the total number of scores can be found by summing up the frequencies for all intervals. From the given histogram, the frequencies for all intervals are 13 + 15 + 17 + 18 + 14 + 12 + 8 = 97. Therefore, the relative cumulative frequency for scores of 20 or lower is 63 / 97 = 0.6495 (rounded to four decimal places).