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# GMAT Statistics 101

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Traversing Averages

In this post will discuss a tip for calculating averages on the GMAT. The average of a list of consecutive integers is the average of any equidistant pair of integers around the median.

For example, take a set of consecutive integers {1, 2, 3, 4, 5}. “3” is the median, and therefore the average.

The use of this insight depends on what data is provided by the question. In many cases, GMAT questions will describe a set of consecutive integers in terms of its first and last terms – all the integers between 22 and 55, for example.

Since the average of the entire group is equal to the average of any pair of integers around the middle, we can use the first and last term provided by the above statement to calculate the average of the entire set.

In other words, the average of the set of all integers between 22 and 55 is simply the average of the first and last terms of the set: the average of 22 and $$55 = \frac{(22+55)}{2} = \frac{77}{2} = 38.5$$. This will also be the median of the set, according to what we’ve already learned of the properties of the average of a set of consecutive integers.

Remember:
For any set of integers with a constant difference between any two consecutive terms (such as consecutive integers or multiples):

Average of the set = Average of any equidistant pair of terms around the median.
From this insight, remember this rule:

Average of a set of consecutive integers = Average of the first and last terms of the set.
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