Bunuel wrote:

The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29

B) 25 ≤ m ≤ 34

C) 30 ≤ m ≤ 39

D) 35 ≤ m ≤ 44

E) 40 ≤ m ≤ 49

We are given a table that has the age categories of the 161 employees at Company X and the number of employees in each category. Recall that if we have a set of n numbers arranged in order, the median of this set of n numbers is the number at the [(n + 1)/2]th position. Thus, the employee with the median age is at the (161+1)/2 = 162/2 = 81st position (assuming the ages of the employees are listed in order). The table provides us with the following information:

Age less than 20: 29 employees (i.e., 1st data point to 29th data point)

Age 20-29: 58 employees (i.e., 30th data point to 87th data point)

We see that the 81st data point will fall into the age group from 20-29 since this age group contains the 30th data point to the 87th data point.

Thus 20 ≤ m ≤ 29.

Answer: A

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