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17 Jun 2016, 05:22
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A
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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
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06 Dec 2016, 08:33
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Bunuel
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
17 Jun 2016, 07:25
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Total number of employees = 161. Thus the median of this set will be the 81st element. Now our job is to find out find range does this element belong to.
if we arrange the set in ascending order, the first 29 elements to set "less than 20".
now the next 58 employees belong to set "20-29". Thus the last element will 29 + 58 = 87th element of the set. And we are supposed to find out the 81st, which will lie in this range, Thus the answer is A.
if we arrange the set in ascending order, the first 29 elements to set "less than 20".
now the next 58 employees belong to set "20-29". Thus the last element will 29 + 58 = 87th element of the set. And we are supposed to find out the 81st, which will lie in this range, Thus the answer is A.
