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# GMAT Math: Arithmetic Mean

Written by Kelly Granson. Posted in GMAT Study Guide GMAT arithmetic mean questions are not very hard, but the GMAT exam is a mixture of simple and more advanced questions. If you perform well, you are most likely to see harder questions, and if your performance is not quite stellar, you will deal mostly with medium and easy test items. However, regardless of your performance, the first few questions will not be exceptionally hard, so chances are you will see at least one GMAT question dealing with arithmetic mean. In this post we will review the very basic info about the arithmetic mean and how it can be tested on the GMAT.

The arithmetic mean is also commonly known as the 'mean' or 'average'. A concept we were all taught in schools from very early age. Nevertheless, let's work through the examples below to refresh ourselves on the basics before we move onto harder questions based upon the arithmetic mean and statistics.

Arithmetic Mean Basic

The literal definition for an arithmetic mean is:

"Arithmetic mean is quotient of sum of the given values and number of the given values".

In basic English, that simply means that the average is the sum of all the values in a set, divided by the total number of values in the same set.

So if we have 5 numbers in a set, let's say for example, 1, 2, 3, 4, and 5, the average is simply: Arithmetic Mean Formula

The equation for the arithmetic mean can be written as: There are many other ways that you will see the equation represented, but if you can remember the wording on the above equation, it will help you to answer many different types of GMAT question. Let's have a look at some examples to see how arithmetic mean works in different cases.

Arithmetic Mean of Negative Numbers

One complication that can be added to GMAT questions testing your knowledge of the arithmetic mean is the addition of negative numbers. Instead of having a set based solely on positive numbers, certain numbers may also be negative. Let's take the same example we had before but make all items in the set negative. The five numbers will now be:

-1, -2, -3, -4, and -5

If we were to work out the arithmetic mean then we would use the same formula: As per the formula, we simply substitute the values:  Note that although the sum of values is now negative, the number of values in the set is always positive.

The exact same process would be used for a mixed number set.

The Missing Number

No matter how nice that would be, GMAT will never just give you a list of numbers and ask you just to find the mean—that's what your sixth grade teacher would do. GMAT, on the other hand, will most likely twist the problem around a little a bit. One common way GMAT tests arithmetic mean is giving you the average and asking to find the missing element of the set.

Let's look at a typical example:

5 students take a test. Amy and Ben both score 20 marks each, Thomas scores 25 marks and Mandy scores 15. What score must Chloe obtain, if the average score is 21 marks.

This question is rather simply when we break it down. Let's extract the key information. Firstly there are five students and four of them have a score:

Amy (A) = 20

Ben (B) = 20

Thomas (T) = 25

Mandy (M) = 15

Chloe (C)= ???

We are given the arithmetic mean as 21. Our objective is to work out Chloe's (C) score. As we know it is an arithmetic mean questions, let's start with the equation and figure out what we know:  Rearranging that equations we get:

Sum of values in a set = 21 × 5

Sum of values in a set = 105

Now we know that the sum of all five scores must equal 105.

Sum of values in a set = A+B+T+M+C=105

We already know four of the scores, so we can immediately substitute them:

20+20+25+15+C=105

80+C=105

A little rearranging will give us our answer:

C=105-80

C=25

Chloe's score is therefore 25.

As you can see, the little twists GMAT adds to the questions can be easily cracked if you know the general formula and can manipulate it. We will look into harder GMAT questions based on the arithmetic mean and statistics in our next posts, so stay updated.

Good luck! 