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# GMAT Statistics 101

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Economist GMAT Tutor Instructor
Joined: 03 Sep 2015
Posts: 49

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19 Apr 2016, 06:57
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GMAT Statistics 101

Three of the most important statistical measures on the GMAT are the mean (or average), median and standard deviation. Familiarize yourself with these terms and these questions will become much easier.

The Mean
To calculate the mean you sum the values in a data set and divide by the number of values. For example, consider the data set 4, 5 and 9. The sum is 18. The number of values in the set is 3. Therefore, the mean is 18 / 3 = 6.

The Median
The median is the middle number in a data set. Consider the following data set: 4, 2, 7, 5, and 1. You determine the median as follows:
* Order the numbers from the smallest number to the largest number.
* 1, 2, 4, 5, and 7.
* The median is therefore 4.

What happens when the number of values in the set is even? For example, 4, 2, 7 and 5.
* Order the numbers.
* 2, 4, 5 and 7.
* Sum the two middle numbers. 4 + 5 = 9.
* Divide by 2. 9 / 2 = 4.5.
* The median is 4.5.

The Standard Deviation
The standard deviation is a measure of how far the values in a data set are from the mean. It can be thought of as the average deviation from the mean.

There is a complicated formula for calculating the standard deviation, but the good news is that we don’t have to use it on the GMAT! However, it is necessary to have a general understanding of what the standard deviation is.

For example, consider the following dataset: 1, 2 and 3. The mean is 2. Now consider a new data set: 0, 2 and 4. The mean is also 2. However, you can see that in the second set the numbers are more widely spread from the mean. Therefore, the second data set has a larger standard deviation.

Questions involving statistical measures are an important part of the GMAT quant section. Be familiar with the meaning of the terms and you will be a long way towards answering these correctly.

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19 Apr 2016, 07:00
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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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19 Apr 2016, 07:03
Median is More Than Just Midpoint

Here we will focus on tricks using the properties of arithmetic sequences. Try your hand at this problem:

A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour it catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did it consume on the sixth hour?
a) 38
b) 47
c) 50
d) 53
e) 62

This is a seemingly tough question, requiring several steps. Fortunately, this question, and others like it, can be solved with the use of the properties of arithmetic sequences.

The question describes an arithmetic sequence with a difference of 3: in the first hour our whale consumes x kilos, in the second (x+3), in the third (x+6), etc. Adding these together will give a total of 450, from which we can find x, but that is not an easy calculation. By the time you’re done with that, you might easily forget that the question does not ask for x, but rather for the consumption in the sixth hour, which is actually x+15.

Instead, recall the average property of arithmetic sequences: Average = Median. Since the question kindly provides the total kilos of Plankton (450) and the number of hours (9), the average hourly consumption of Plankton can be easily calculated: 450 / 9 = 50.

Therefore, the median of our set of consecutive integers is also 50. Since the set has an odd number of members, the median is the number in the middle, or the 5th hour. If the whale consumes 50 kilos of Plankton in the 5th hour, he will consume 50+3 = 53 kilos in the sixth hour.

Quick and easy – with the right approach.

This question is discussed HERE.
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19 Apr 2016, 07:09
Other Resources on Statistics

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31 Jan 2018, 02:09
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