If the sum of a list of temperatures is divided by the average (arithmetic mean) of the temperatures, the quotient is z. What does z represent?
A. The average of the temperatures
B. The sum of the temperatures
C. Half the average of the temperatures
D. Two times the sum of the temperatures
E. The number of temperatures
Read the problem carefully. Be sure that you consider the meaning of all the terms in this problem. For instance, it is important to remind yourself that a quotient is the result when one number is divided by another.
Identify the bottom line. What does z represent?
Assess your options. There are two ways to solve this problem. Your first option is to “think” though the problem in order to figure out what the variable z refers to. Your second option is to pick numbers, which will make the problem much more concrete if you have trouble thinking about mathematical concepts abstractly. The latter option is the easier of the two, so that is the one we will illustrate here.
Attack the problem. The first thing you should do any time you see an average problem is to write out the average formula:
Next, pick two numbers: a larger one to be the sum of all the temperatures, and a smaller one to be the number of temperatures. Pick easy numbers, and make sure that the smaller number is a factor of the larger number so that it will divide in evenly. Let’s use 12 as the sum of the temperatures and 3 as the number of temperatures. If you plug these two numbers into the average formula, the average of the temperatures will come out to be 4.
The problem asks you to find the quotient (z) when the sum of the temperatures is divided by the average of the temperatures. Plug in the numbers you have chosen to find the result.
The result is 3, which is the number of temperatures. Pick the answer choice that matches with this solution.
The correct answer is (E).
This is a medium-level problem.