At State University, the average (arithmetic mean) salary of

Step 1 of the Kaplan Method for DS: Analyze the stem

We see that there are only two groups, and we know the average of each individual group. We're asked to find the overall average.

We think: to solve for a weighted average, we need the weighting of each group.

Step 2 of the Kaplan Method for DS: Evaluate the statements

(1) tells us the total number of professors, but not how many are in each group: insufficient, eliminate A and D.

(2) tells us that there are twice as many profs in the philosophy department; in other words, the philosophy profs make up 2/3 of all of the professors. We now know the weight of each group: sufficient, eliminate C and E; choose B!

If we actually wanted to solve (say this were a problem solving question), we'd do so as follows:

Overall average of a group = (avg group 1)(weight group 1) + (avg group 2)(weight group 2) + ... + (avg group n)(weight group n)

Overall salary average = (avg salary phil profs)(weight of phil profs) + (avg salary bus profs)(weight of bus profs)

Overall salary average = (56000)(2/3) + (74000)(1/3) = 112000/3 + 74000/3 = 186000/3 = 62000

(There are other, quicker, ways to solve using weighted averages, but applying the formula is the "textbook" approach.)

Whenever you review a question (and you should review every one you do!), you always want to finish by asking "what can I take away from this exercise?" Here are our takeaways from this question:

1) to solve for an overall average, you don't necessarily need the numbers in each group - knowing the weights of each group is sufficient;

2) the better you understand the concepts, the less math you'll need to do on test day; and

3) it's better to be a business prof than a philosophy prof!