Help with Weighted means... Please!!

#1
Hello! I understand the concept of a weighted mean... when it is applied to things such as grade point averages and the like. There is a problem in my homework today that has me baffled though because it doesn't make sense to me.

I am told to find the weighted mean of the data... then this is the problem given: "The average starting salaries (by degree attained) for 25 empoyees at a company are given. What is the mean starting salary for these employees?

8 with MBA's: 42,500
17 with BA's in business: 28,000

That is the only information given... how am I supposed to find a weighted mean with only that info? Anyone see something I am missing?

Thanks
~Jes
 
#2
Hi Jes,

I hope it's not too late to answer your question.

All the information you need is given in the problem. Consider the following (not correct) way of finding the average salary:

"So the MBA's get 42K and the BA's get 28K. That means the average is 42+28/2 = 70/2 = 35K" [Again, this is wrong]

You have more information than this, namely:

Total Employees: 25
8 MBA's @ 42.5K on average
17 BA's @ 28K on average

Using this information, think about the company's entire payroll (in dollars) divided by its total number of employees. This will give you the mean salary for the average joe (regardless of degree).

Again:

mean salary = total payroll/number of employees

Actually, to build on your understanding of weights in calculating GPA, consider this formula for calculating a GPA:

Average GPA = (Grade1 * Units1) + (Grade2 * Units2) + ... + (GradeN * UnitsN) / Total Units

So if I have these grades and my classes vary between 3 and 4 units:

GPA = (4.0 * 4) + (3.0 * 3) + (3.5 * 4)/11 = 39/11 = 3.54

Hope you see the analogy with the business example
 
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