Question

the following relative frequency table shows reasons given by high school students for their last absence from school.

reason	relative frequency
overslept	0.20
college visit	0.16
did not finish assignment	0.07

which of the following statements is not supported by the relative frequency table?

a more than half the students were absent because of illness.

b more than one - third of the students were absent because of oversleeping or college visits.

c the reason given the least number of times was did not finish assignment.

d only 7 students were absent because they did not finish an assignment.

e less than one - fourth of the students were absent because they overslept.

Explanation:

Step1: Analyze Option A

The relative frequency for illness is \( 0.57 \), which is more than \( 0.5 \) (half). So A is supported.

Step2: Analyze Option B

Relative frequency for oversleeping is \( 0.20 \), for college visit is \( 0.16 \). Sum: \( 0.20 + 0.16 = 0.36 \), which is more than \( \frac{1}{3}\approx0.333 \). So B is supported.

Step3: Analyze Option C

The least relative frequency is \( 0.07 \) (did not finish assignment), so the reason with least frequency is did not finish assignment. C is supported.

Step4: Analyze Option D

We don't know the total number of students, so we can't say "only 7 students" (since relative frequency is \( 0.07 \), total students \( n \) would mean \( 0.07n = 7\Rightarrow n = 100 \), but total isn't given). So D is not supported.

Step5: Analyze Option E

Relative frequency for oversleeping is \( 0.20 \), which is less than \( 0.25 \) (one - fourth). So E is supported.

Answer:

D. Only 7 students were absent because they did not finish an assignment.