Aside from the standard average formula (which you should know very well), there is another property of averages that is often tested in the Quantitative Comparison format. Try an example:
| A company has two divisions. Division A has 105 employees and an average salary of $60,000. Division B has 93 employees and an average salary of $70,000. |
|
| Quantity A | Quantity B |
| The average salary of all the employees at the company |
$65,000 |
A lot of unnecessary computation could go into answering this QC question. Notice that your benchmark value in Quantity B is exactly halfway between the average salaries of the two divisions. This is very convenient because you can use the principle of weighted averages.
Suppose that instead of 198 employees (105 + 93), you have six employees: three people in each division. To simplify things, you can say that everyone in Division A makes $60,000 and everyone in Division B makes $70,000.
The average salary for all 6 employees will be:
There are an equal number of people in each division, so the average salary is the average of 60,000 and 70,000.
Think of average salaries as a spectrum. There are three scenarios:
The common information tells you there are more employees in Division A (105 vs. 93). The average salary of the whole company will be less than $65,000:
| Quantity A | Quantity B |
| The average salary of all the employees at the company = less than $65,000 |
$65,000 |
The correct answer is (B).
If two groups have an equal number of members, the total average will be the average of the two groups
(e.g.,
).
If one group has more members, the total average will be closer to the average of that group
(e.g.,
). There’s no need to do this calculation!