GRE Math Strategy : MEAN, MEDIAN, MODE, RANGE,Standard Deviation {Simple Approach}

GRE Math Strategy : MEAN, MEDIAN, MODE, RANGE,Standard Deviation  {Simple Approach}

Arithmetic Mean

The mean of a set of numbers (sometimes called arithmetic mean) is simply the average of the numbers. The words mean, arithmetic mean, and average all have the same meaning. When a problem asks for the mean or arithmetic mean, you can use this formula:

Average = Sum of Terms / Number of Terms

For example, the average of the numbers 7, 5 and 12 is (7+5+12) / 3 = 24/3 = 8

If you encounter a problem that is not quite so straightforward, it helps to remember that mean and sum are closely related. Look what happens when you rewrite the formula for the average:

Average = Sum of Terms / Number of Terms

Number of Terms = Average x Sum of Terms

So, the sum is the product of the number of terms and the average. In the example above, 3 x 8 = 24. Consider how this relationship is used in the following problem.

Example Problem:

Nancy shopped at four department stores and spent an average of $80 per store. If she wants to average no more than $70 per store over a total of six stores, what is the most she can average at the two remaining stores?

A) $40

B) $50

C) $55

D) $65

E) $70

This problem might be difficult if you try to approach it by looking for an average, but if you use the formula for the sum of terms, it is not difficult.

Nancy has spent an average of $80 per store at four stores, or a sum of $4 x $80 = $320.

Her limit is an average of $70 per store at six stores, or a sum of 6 x $70 = $420.

This means she can spend $100 at the two remaining stores, or an average of $100/2 = $50 per store. Choice (B) is Correct

Median

" Median = middle term " (ordered  list of elements )

The median of a set is the middle term when all the terms in the set are listed in sequential order. When there is an even number of terms in a set, the median is the average of the two middle terms.

To find the median of the set 4, 7, 5, 23, 5, 67, 10, first arrange the terms in order: {4, 5, 5, 7, 10, 23, 67}. The median is the middle term, 7. Now suppose the set contained one more term, say an 8. The set would be {4, 5, 5, 7, 8, 10, 23, 67}, and the median would be the average of the two middle terms, or ( 7 + 8 )/2 =15/2 = 7.5

Mode

" Mode = the term that occurs most frequently "

The mode of a set is simply the term that occurs most frequently. For the set {4, 5, 5, 7, 70, 23, 67}, the mode is 5 because 5 occurs the greatest number of times. If one of the 5s were removed, the set would be {4, 5, 7, 70, 23, 67), which has no mode. If another 10 were included in the original set, the set would be {4, 5, 5, 7, 10, 10, 23, 67},and both 5 and 10 would be modes.

Range

" Range = greatest term - least term "

The range of a set is simply the difference between the greatest term and the least term. For the set {4, 5, 5, 7, 10, 23, 67}, the range is 67 - 4=63

Standard Deviation

" Standard deviation refers to how far apart the numbers in a set are from one another "
The closer the numbers are to each other, the smaller the standard deviation will be. The more spread out the numbers are from each other, the larger the standard deviation will be.

Here are the steps needed to calculate the standard deviation:
. Calculate the average (arithmetic mean) of the set
. Determine the difference between each number and the average
. Square these differences
. Add the results and divide by the number of terms to determine the average
. Take the square root of the average

Summary: