Re: Each employee of a certain company is in either Department X or Depart
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12 Apr 2024, 16:20
Let's use weighted averages
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
There are more than twice as many employees in Department X as in Department Y
Let's see what happens if there are EXACTLY twice as many employees in Department X as in Department Y
So, for every 3 employees, 2 work for Department X and 1 works for Department Y
In other words, 2/3 of the employees work for Department X
And 1/3 of the employees work for Department Y
The average (arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y
So, the average salary of ALL employees = (2/3)($25,000) + (1/3)($35,000)
≈ $28,333
So, the average salary of all employees = $28,333 if there are EXACTLY twice as many employees in Department X as in Department Y
Now let's see what happens if we MAXIMIZE the number of employees working for Department X
Let's say that ALL of the employees work for Department X
So, 1/1 employees work for Department X, and 0/1 employees work for Department Y
Now, the average salary of ALL employees = (1/1)($25,000) + (0/1)($35,000)
≈ $25,000
So, the average salary of all employees = $25,000 if there ALL of the employees work in Department X
Now that we've examined the EXTREME cases, we know that the average salary of all employees is BETWEEN $25,000 and $28,333
Answer: A, B