# GRE Subject Test: Math : Mean

## Example Questions

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### Example Question #4 : Other Topics

Find the mean of the following set of numbers:

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:

### Example Question #5 : Other Topics

The mean of four numbers is .

A: The sum of the four numbers.

B:

Quantity B is greater.

Both are equal.

Can't be determined from the given information.

Quantity A is greater.

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 #6 : Other Topics

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

A: Mean of .

B: Mean of

Quantity B is greater.

Both are equal.

Quantity A is greater.

Can't be determined from the information above.

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 #7 : Other Topics

If  and are positive integers from  inclusive, then:

A: The mean of

B: The mean of

Both are equal

Quantity A is greater

Can't be determined from the information above

Quantity B is greater

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 #8 : Other Topics

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:

Quantity A is greater

Both are equal

Quantity B is greater

Can't be determined from the information above

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 #9 : Other Topics

Find the mean.

Explanation:

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

### Example Question #10 : Other Topics

Find   if the mean of  is .

Explanation:

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

Cross-multiply.

Subtract  on both sides.

### Example Question #11 : Other Topics

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

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 #1 : Mean

What is the average of the first ten prime numbers?

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 #13 : Other Topics

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

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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