# GRE Subject Test: Math : Probability & Statistics

## Example Questions

### Example Question #1 : Mean

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 #11 : Probability & Statistics

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 #1 : Statistics

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 .

### Example Question #11 : Mean

John has math test scores of . What could be his final test score if he wants the average of his exams to be at least ?

Explanation:

To find the missing value, we add the terms up and divide them by  to have the average of .

Cross-multiply.

Subtract both sides by

Since the question is asking for a test score that will generate AT LEAST average of , we look for an answer that is greater than  which is

### Example Question #12 : Mean

Sam has math test scores of . The teacher drops the lowest test score except the final and the highest test score is counted as two exams. If Sam took his final exam and felt he scored between  inclusive, what is the lowest possible average of his exams?

Explanation:

We have four test scores of . We know the range of the final exam is  so therefore the  is counted twice. Since the final exam grade regardless if the lowest possible value can't be dropped, this means we drop the  and include the lowest possible test score which is . So the mean is:

### Example Question #13 : Mean

There were  exams graded. The average of the exams were . If the average of  exams were , what was the average of the remaining exams?

Explanation:

With  exams of average , the sum of the scores were .

We already know the first  exams with average of . Therefore, the sum is .

The remaining number of exams is  or .

The remaining sum is  or .

We divide  by  to get

### Example Question #11 : Other Topics

What is the mean of the scores 95, 13, 67, 89, 13, 45, and 109?

Explanation:

To get the average or mean, add up all the scores and then divide by the number of scores.

There are seven scores so divide that number by 7

### Example Question #14 : Mean

Find the mean of the set of numbers containing: .

Explanation:

Step 1: We need to know how to find mean. To find mean, add up all the numbers in the set and divide by how many numbers are in the set.

Step 2: Let's find the sum:

.

Step 3: Count how many numbers are in the set.

..There are 9 numbers.

Step 4: Divide the sum by 9 to find the average.

.

The average of the set of numbers is

### Example Question #15 : Mean

What is the mean of ?

Explanation:

Step 1: Find the sum of all the numbers.

Step 2: Divide the sum by how many numbers there are. There are 11 numbers.

The mean (average) of all numbers above is .

### Example Question #17 : Mean

What is the mean of