GRE Subject Test: Math : Mean

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

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Example Question #1 : Mean

Find the mean of the following set of numbers:

 

Possible Answers:

Correct answer:

Explanation:

The mean can be found in the same way as the average of a group of numbers. To find the average, use the following formula:

So, if our set consists of 

We will get our mean via:

So our answer is

Example Question #2 : Mean

The mean of four numbers is .

A: The sum of the four numbers.

B: 

Possible Answers:

Can't be determined from the given information.

Both are equal.

Quantity B is greater.

Quantity A is greater.

Correct answer:

Both are equal.

Explanation:

To find the sum of the four numbers, just multiply four and the average. By multiplying the average and number of terms, we get the sum of the four numbers regardless of what those values could be.

 Since Quantity A matches Quantity B, answer should be both are equal. 

Example Question #3 : Mean

Mean of  is  are all positive integers.  is between  and  inclusive. 

A: Mean of .

B: Mean of 

Possible Answers:

Both are equal. 

Can't be determined from the information above.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Can't be determined from the information above.

Explanation:

Let's look at a case where .

Let's have  be  and  be . The sum of the three numbers have to be  or 

The average of  is  or . The avergae of  is  or .

This makes Quantity B bigger, HOWEVER, what if we switched the  and  values. 

The average of  is still  or . The avergae of  is  or .

This makes Quantity A bigger. Because we have two different scenarios, this makes the answer can't be determined based on the information above.

Example Question #3 : Mean

If  and are positive integers from  inclusive, then:

A: The mean of 

B: The mean of 

Possible Answers:

Quantity A is greater

Can't be determined from the information above

Quantity B is greater

Both are equal

Correct answer:

Can't be determined from the information above

Explanation:

Let's add each expression from each respective quantity

Quantity A: 

Quantity B: 

Since  we will let  and . The sum of Quantity A is  and the sum of Quantity B is also . HOWEVER, if  was , that means the sum mof Quantity B is . With the same number of terms in both quantities, the larger sum means greater mean. First scenario, we would have same mean but the next scenario we have Quantity B with a greater mean. The answer is can't be determined from the information above. 

Example Question #5 : Statistics

John picks five numbers out of a set of seven and decides to find the average. The set has 

A: John averages the five numbers he picked from the set.

B: 

Possible Answers:

Both are equal

Can't be determined from the information above

Quantity B is greater

Quantity A is greater

Correct answer:

Quantity B is greater

Explanation:

To figure out which Quantity is greater, let's find the highest possible mean in Quantity A. We should pick the  biggest numbers which are . The mean is . This is the highest possible mean and since Quantity B is  this makes Quantity B is greater the correct answer.

Example Question #4 : Mean

Find the mean.

Possible Answers:

Correct answer:

Explanation:

To find the mean, add the terms up and divide by the number of terms.

Example Question #5 : Mean

Find   if the mean of  is .

Possible Answers:

Correct answer:

Explanation:

To find the mean, add the terms up and divide by the number of terms.

 Then add the numerator.

 Cross-multiply.

 Subtract  on both sides.

Example Question #6 : Mean

If average of  and  is  and  is  what is the average of ?

Possible Answers:

Correct answer:

Explanation:

If the average of  and  is , then the sum must be 

If we add the sum of  we get  or .

To find the average of the three terms, we divide  and  to get 

Example Question #7 : Mean

What is the average of the first ten prime numbers?

Possible Answers:

Correct answer:

Explanation:

The first ten prime numbers are . Prime numbers have two factors:  and the number itself. Then to find mean, we add all the numbers and divide by .

Example Question #8 : Mean

If the average of seven consecutive numbers is , what is the value of the second number in the set?

Possible Answers:

Correct answer:

Explanation:

There are two methods.

Method 1:

Since the average of  consecutive number is , we can express this as:

 Cross-multiply

 Subtract  on both sides then divide both sides by 

 Since we are looking for the second term, just plug into expression . That means answer is  or 

Method 2:

Since the average of  consecutive number is , this means the median is also . Consecutive means one after another and with each term having the same difference, we know the mean equals the median. Since there are  terms, the median will have  terms left and right of it. Then, the series will go . The second term is .

 

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