The ages of the machines in one of the production lines in your company are exhibited in the frequency distribution table below. Two additional machines have been added to the production line,and the median age of the machines didn't change.
What is the minimum number of new (0-year-old)machines that you need to purchase to change the median age of the machines?
A) 1
B) 2
C) 3
D) 4
E) 5

Question

The ages of the machines in one of the production lines in your company are exhibited in the frequency distribution table below.  Two additional machines have been added to the production line,and the median age of the machines didn't change.
What is the minimum number of new (0-year-old)machines that you need to purchase to change the median age of the machines?
A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Quizplus · Accepted Answer

The median of the current data set is the value at the 15th position, which is 14 years. Since the median did not change after adding two new machines, we know that both of these machines must also have an age of 14 years.

To change the median, we need to add at least one machine with an age less than 14 years. If we add one new machine with an age of 8 years, then the median will become (14+8)/2 = 11 years.

Therefore, the minimum number of new machines we need to purchase to change the median age of the machines is 2, or answer choice B.

The Ages of the Machines in One of the Production