Question

in a student survey, forty-one part-time students were asked how many courses they were taking this term. the (incomplete) results are shown below.
a. fill in the missing values. please round your answer to 4 decimal places for the relative frequency if possible.

# of courses	frequency	relative frequency	cumulative frequency
2		0.439	28
3	13		41

b. what percent of students take exactly one courses? give your answer as a percent, rounded to the nearest hundredth. %

Explanation:

Part a

Step 1: Find the frequency for 2 courses

We know that cumulative frequency for 2 courses is 28, and cumulative frequency for 1 course is its frequency (since it's the first category). So frequency for 2 courses = Cumulative frequency for 2 - Frequency for 1 = \(28 - 10 = 18\)

Step 2: Find the relative frequency for 3 courses

Relative frequency is calculated as \(\frac{\text{Frequency}}{\text{Total number of observations}}\). Total number of students is 41. So relative frequency for 3 courses = \(\frac{13}{41} \approx 0.3171\) (rounded to 4 decimal places)

Step 3: Find the cumulative frequency for 1 course

Cumulative frequency for 1 course is just its frequency, so it's 10.

Part b

Step 1: Convert relative frequency of 1 course to percentage

The relative frequency for 1 course is 0.2439. To convert to percentage, we multiply by 100: \(0.2439\times100 = 24.39\%\)

Final Answers

Part a

• Frequency for 2 courses: \(18\)
• Relative frequency for 3 courses: \(0.3171\)
• Cumulative frequency for 1 course: \(10\)

Part b

\(24.39\%\)

Answer:

Part a

Step 1: Find the frequency for 2 courses

We know that cumulative frequency for 2 courses is 28, and cumulative frequency for 1 course is its frequency (since it's the first category). So frequency for 2 courses = Cumulative frequency for 2 - Frequency for 1 = \(28 - 10 = 18\)

Step 2: Find the relative frequency for 3 courses

Relative frequency is calculated as \(\frac{\text{Frequency}}{\text{Total number of observations}}\). Total number of students is 41. So relative frequency for 3 courses = \(\frac{13}{41} \approx 0.3171\) (rounded to 4 decimal places)

Step 3: Find the cumulative frequency for 1 course

Cumulative frequency for 1 course is just its frequency, so it's 10.

Part b

Step 1: Convert relative frequency of 1 course to percentage

The relative frequency for 1 course is 0.2439. To convert to percentage, we multiply by 100: \(0.2439\times100 = 24.39\%\)

Final Answers

Part a

• Frequency for 2 courses: \(18\)
• Relative frequency for 3 courses: \(0.3171\)
• Cumulative frequency for 1 course: \(10\)

Part b

\(24.39\%\)