Question

There are 21 students in a class. The median age of the students is 23. The oldest student is 29.
Based on this information, what is the truthfulness of each statement in the table? Select the phrase that best describes each statement.
Statement
Truthfulness
At least one student is 23. Must be true could be true cannot be true
Some students are younger than 15. Must be true could be true cannot be true

Answer 1

Answer:

1) At least one (the 11th) student is 23 (years old), Must be true

2) Some students are younger than 15 Could be true

Step-by-step explanation:

1) The given parameters are;

The number of student in the class = 21

The median age of the student = 23

The age of the oldest student = 29

Therefore, given that the median age = The age of the (n + 1)/2 th student

Where;

n = The number of student in the class = 21

∴ The median age = The age of the (21 + 1)/2 th = 11 th student, when the age of the students are arranged in increasing order, therefore, we have;

At least one (the 11th) student is 23 (years old), Must be true

2) Given that there are 10 students with ages equal to or lower than the  median age, and the difference between the median age and the age of the oldest student = 29 - 23 = 6 years, we have;

Some students are younger than 15 Could be true