# ISEE Upper Level Math : Mean

## Example Questions

### Example Question #61 : Data Analysis And Probability

The heights of a football team's members are  and  inches. Find the mean of the heights.

Explanation:

The mean is the sum of all the data values divided by the number of values. So we can write:

### Example Question #61 : Data Analysis

Consider the following set of scores from a physics test. Give the mean of the scores.

Explanation:

The mean of the scores can be calculated as:

Where:

is the mean of a data set, indicates the sum of the data values  ,  and  is the number of data values. So we can write:

### Example Question #61 : Data Analysis

The mean of five numbers is . Give their sum.

Explanation:

The mean of five numbers is equal to their sum divided by , or as a formula we can write:

Where:

is the mean of a data set, indicates the sum of the data values  ,  and  is the number of data values. So we can write:

### Example Question #63 : Data Analysis

The sum of numbers is . Find the mean in terms of . ( is a real number)

Explanation:

The mean of eight numbers is equal to their sum divided by  or as a formula we can write:

### Example Question #64 : Data Analysis

In the following set, find the mean in terms of .

Explanation:

The mean of the scores can be calculated as:

Where:

is the mean of a data set, indicates the sum of the data values  ,  and  is the number of data values. So we can write:

### Example Question #65 : Data Analysis

The sum of a set of values is . If the mean of the data set is , give the number of values in the set.

Explanation:

Mean of the scores can be calculated as:

Where:

is the mean of a data set, indicates the sum of the data values  ,  and  is the number of data values. So we can write:

### Example Question #61 : Data Analysis And Probability

The mean of test scores is . When the student takes the test, the mean goes down by two points. Give the score.

Explanation:

The total of test scores is . The mean of the total scores for students would be:

Where:

is the mean of a data set, indicates the sum of the data values and is the number of data values. So we can write:

### Example Question #71 : Data Analysis

The sum of test scores is . When the student takes the test, the mean of the scores does not change. Give the score of the student.

Explanation:

The mean is the sum of the data values divided by the number of values or as a formula we have:

Where:

is the mean of a data set, indicates the sum of the data values and is the number of data values. So we have:

When the student takes the test the mean of the score does not change. Let:

student score. So we can write:

That means the student should get the score of which is equal to the initial mean in order to get the same value for the new mean.

### Example Question #71 : Data Analysis

The sum of test scores is . When the student takes the test and gets a score of , how does the mean change?

The mean goes up by  points.

The mean goes down by  points.

The mean goes up by points.

The mean goes down by points.

The mean goes down by  points.

The mean goes down by points.

Explanation:

The mean is the sum of the data values divided by the number of values or as a formula we have:

Where:

is the mean of a data set, indicates the sum of the data values and is the number of data values. The total of test scores is ; the mean of the scores is:

When the student takes the test the sum of scores would be and the new mean of the scores is:

### Example Question #71 : Data Analysis

A gymnastics meet has seven judges. After each routine, each judge assigns a merit-based score from 0 to 10; a contestant's score for the routine is the mean of all the judges' scores except for the highest and the lowest.

The seven judges individually assigned the following scores to one of Donna's routines: . What is Donna's score, rounded to the nearest tenth?