How many students had scores lower than X = 80? X: 90-94, 85-89, 80-84, 75-79, 70-74; F: 3, 4, 5, 2, 1

How many students had scores lower than X = 80? X: 90-94, 85-89, 80-84, 75-79, 70-74; F: 3, 4, 5, 2, 1

• A. 2
• B. 3
• C. 7
• D. Cannot be determined

Answer: (B)

When reading a grouped frequency distribution, to find how many students scored below a cutoff you add the frequencies of all classes that lie entirely below that cutoff. Since scores must be strictly less than 80, we include only the ranges below 80: 75–79 and 70–74. Their frequencies are 2 and 1, respectively, giving a total of 3 students. The 80–84 range is not included because it starts at 80, which is not below 80, and higher ranges exceed the cutoff. So the number of students scoring below 80 is 3.

When reading a grouped frequency distribution, to find how many students scored below a cutoff you add the frequencies of all classes that lie entirely below that cutoff. Since scores must be strictly less than 80, we include only the ranges below 80: 75–79 and 70–74. Their frequencies are 2 and 1, respectively, giving a total of 3 students. The 80–84 range is not included because it starts at 80, which is not below 80, and higher ranges exceed the cutoff. So the number of students scoring below 80 is 3.