The average age of a class is 16. If two students aged 17 and 15 leave the class, which of the following is true about the new average age?
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The average will not change as the average of the students leaving the class is also 16.
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The average will decrease because of the decrease in the total number of students.
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The average will increase because of the change in the number of students and the total age.
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Nothing can be said about the new average without knowing the exact number of students.
The average age of the class is 16. When two students with ages 17 and 15 leave, their combined age is 32, which is exactly 2 times the average of 16. Since the sum of the ages of the students leaving is equal to the original average multiplied by the number of students leaving, the total sum of the remaining ages divided by the new count remains 16.
The average age of the class remains unchanged when departing students have an average age exactly equal to the class average. The two leaving students have ages of 17 and 15, and their average is the sum of 17 and 15 divided by 2, which equals 16. Since this matches the class average, subtracting their combined ages from the total does not change the overall average.