Question

Suppose that 65 students were asked how many courses they were taking this semester. The (incomplete) results are shown below. Fill in the blank cells to complete the table. Round the relative frequencies to the nearest tenth. Number of Courses 1 2 3 Frequency 15 20 __ Relative Frequency 0.2 _ _ _.

Answer 1

The missing frequency for students taking 3 courses is 30 and the relative frequencies for taking 2 courses and 3 courses are 0.3 and 0.5 respectively when rounded to the nearest tenth. The table is completed using the total number of students, which is 65.

Step-by-step explanation:

To complete the table with the missing frequency and relative frequencies, we need to consider that the total number of students surveyed is 65. Given that there are 15 students taking 1 course and the relative frequency is 0.2, we can calculate the relative frequency for the 20 students taking 2 courses. The relative frequency is calculated by dividing the frequency by the total number of students. Therefore, for 2 courses, the relative frequency is 20/65 which rounds to 0.3 when rounded to the nearest tenth.

With 15 students taking 1 course and 20 students taking 2 courses, this leaves us with 65 - 15 - 20 = 30 students that must be taking 3 courses. To find the relative frequency for 3 courses: 30/65 = 0.46 which rounds to 0.5 when rounded to the nearest tenth. Now we have all the missing values in the table.

The completed table shows that 15 students are taking 1 course with a relative frequency of 0.2, 20 students are taking 2 courses with a relative frequency of 0.3 and 30 students are taking 3 courses with a relative frequency of 0.5, adding to a total of 65 students surveyed.