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GMAT Statistics: Mode, Median, Range

Written by Kelly Granson. Posted in GMAT Study Guide

There is a good chance that you will not even have to deal with a statistics-based question during your GMAT exam as such questions rarely appear on the test. But if you have a general understanding of what statistical terms mean, these questions are usually straightforward and quick to answer. In this article, we will look at three simple concepts within statistics, namely, mode, range and median.

Mode

The mode is a very simple term to understand. It is the number that appears most often in a set of numbers.

Calculating the mode is a lot less complex than performing other statistical calculations. The mode is found by counting the number of times each number appears in a set. The mode is then the number that appears most often (or numbers if there is a tie).

Let's try to identify the mode in this set of numbers.

1, 4, 5, 6, 4, 2, 3, 9, 8, 4, 5

All we have to do is establish how many times each number appears in the set: number 1 appears once, number 2 once, number 3 once, number 4 three times, number 5 twice, number 6 once, number 8 once, and number 9 once.

The number that occurs the most times is 4, and it is, therefore, our mode, the most common number in the set.

Range

The range is another very simple term to understand. Range simply means the difference between the largest and smallest values.

In order to calculate the range, you simply need to subtract the smallest number from the largest number in a set. Using the set of numbers above, we can calculate the range by subtracting the smallest number (1) from the largest number (9), giving us a range of 8. The formula for calculating the range is:

Range=largest number-smallest number

Median

The median value is the number that is located in the middle of a set of numbers when that set is ordered from the smallest number to the largest.

It has to be noted that where there is an odd number of values in a set, the median is the middle number. When we have an even number of values in a set, the median is the average of the two middle numbers.

For example, in this set of five values:

2, 4, 6, 8, 10

the median is 6.

However, in this set of six values:

2, 4, 6, 8, 10, 12

the median lies between 6 and 8. Therefore, calculating the average of 6 and 8 will give us the median:

Quite often numbers will not be presented in ascending order, so our first task will always involve ordering the numbers.

Let us try a GMAT exam style statistics question:

If x< 7, what is the median of a set 8, 7, 8, 9, 11, 12, 4, x?

The first step is to order the values in ascending order:

4, x, 7, 8, 8, 9, 11, 12

We do not know the exact value of x, but we know is that it is less than 7. So, we will put it before 7. No need to calculate x. Since there is an even number of values in this set, the median will be the average of the middle two values. It does not matter if x is greater or less than 4, as the middle two numbers in the sequence will always stay the same. Since the middle two numbers are two 8s, the average of the middle two numbers will give us our median, which will also be 8.

It is rare within a GMAT exam for a question to focus solely on range or mode. More often you will see GMAT statistics questions combining these concepts with the median and mean. Be sure to solve different types of statistics-based GMAT questions so that, when the time comes, you are ready.

Good luck!