# GMAT Math : Calculating arithmetic mean

## Example Questions

### Example Question #11 : Arithmetic Mean

Consider the following set of numbers:

85, 87, 87, 82, 89

What is the mean?

Explanation:

### Example Question #2031 : Problem Solving Questions

Consider the following set of numbers:

85, 87, 87, 82, 89

What is the median?

Explanation:

Reorder the values in numerical order:82, 85, 87, 87, 89

The median is the center number, 87.

### Example Question #11 : Calculating Arithmetic Mean

Find the mean of the sample data set.

Explanation:

The mean of a sample data set is the sum of all of the values divided by the total number of values. In this case:

### Example Question #12 : Arithmetic Mean

The average of the following 6 digits is 75. What is a possible value of ?

80, 78, 78, 70, 71,

Explanation:

Therefore, the sum of all 6 digits must equal 450.

Subtract 377 from both sides.

### Example Question #12 : Arithmetic Mean

When assigning a score for the term, a professor takes the mean of all of a student's test scores except for his or her lowest score.

On the first five exams, Donna has achieved the following scores: 76, 84, 80, 65, 91. There is one more exam in the course. Assuming that 100 is the maximum possible score, what is the range of possible final averages she can achieve (nearest tenth, if applicable)?

Minimum 79.2; maximum 99.2

Minimum 80, maximum 84

Minimum 66; maximum 71.8

Minimum 79.2; maximum 86.2

Minimum 66; maximum 99.2

Minimum 79.2; maximum 86.2

Explanation:

The worst-case scenario is that she will score 65 or less, in which case her score will be the mean of the scores she has already achieved.

The best-case scenario is that she will score 100, in which case the 65 will be dropped and her score will be the mean of the other five scores.

### Example Question #13 : Arithmetic Mean

What is the mean of this data set?

Explanation:

Add the numbers and divide by 6:

### Example Question #11 : Arithmetic Mean

If  and , then give the mean of , and .

Insufficient information is given to answer this question.

Explanation:

The mean of , and  is

If you add both sides of each equation:

or

Equivalently,

,

making 290 the mean.

### Example Question #11 : Arithmetic Mean

What is the mean of the following data set in terms of  and ?

Explanation:

Add the expressions and divide by the number of terms, 8.

The sum of the expressions is:

Divide this by 8:

### Example Question #31 : Descriptive Statistics

Julie's grade in a psychology class depends on three tests, each of which are equally weighted; one term paper, which counts half as much as a test; one midterm, which counts for one and one-half as much as a test; and one final, which counts for twice as much as the other tests.

Julie has scored 85%, 84%, and 74% on her three tests, 90% on her term paper, and 72% on her midterm. She is going for an 80% in the course; what is the minimum percent she must score on the final (assuming that 100% is the maximum possible) to achieve this average?

%

%

%

%

She cannot achieve this average this term.

%

Explanation:

Let  be her final grade. Julie's final score is calculated as a weighted mean, so we can set up the following inequality:

Simplify and solve for :

Julie must make a minimum of 82% on the final to meet her goal.

### Example Question #11 : Arithmetic Mean

Consider this data set:

Order the mean, median, mode, and midrange of the data set from least to greatest.

Midrange, median, mean, mode

Median, mean, midrange, mode

Midrange, mean, median, mode

Mean, median, midrange, mode

Median, midrange, mean, mode

Midrange, mean, median, mode

Explanation:

The mean of the data set is the sum of the elements divided by the size of the set, which is ten:

The median of a data set with an even number of elements is the arithmetic mean of the two elements that fall in the middle when the elements are arranged in ascending order. These two elements ar 6 and 7, so the median is

The mode of the data set is the element which occurs the most frequently. Since 7 appears three times, 6 appears twice, and all other elements appear once, the mode is 7.

The midrange of the data set is the arithmetic mean of the least and greatest elements. These two elements are 1 and 10, so the midrange is .

The four quantities, in ascending order, are:

Midrange, mean, median, mode.