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# Mean, Median, Mode, and Graphs Study Guide for McGraw-Hill's ASVAB

By McGraw-Hill Professional
Updated on Mar 16, 2011

### Mean, Median, and Mode

The mean, median, and mode are mathematical measures that are used to understand and describe a given set of numbers.

Mean or Average   The mean of a set of numbers is the average. Add the numbers and divide by the number of numbers.

Examples

What is the mean of the numbers 2, 4, 7, 4, and 5?

The sum is 22. Since there are 5 numbers, divide 22 by 5 to get a mean or average of 4.4.

What is the mean of the numbers 3, 4, 2, 6, 7, 12, 56, and 104?

The sum is 194. There are 8 numbers, so divide 194 by 8 to get 24.25.

Median   Order a set of numbers from least to greatest. If there is an odd number of numbers, the median is the number in the middle of that sequence of numbers. If there is an even number of numbers, the median is the mean or average of the two middle numbers.

Examples

What is the median of the following numbers?

14, 999, 75, 102, 456, 19, 10

Reorder the numbers from least to greatest: 10, 14, 19, 75, 102, 456, 999

The middle number is 75, so that is the median.

What is the median of the following numbers?

15, 765, 65, 890, 12, 1, 10

Reorder the numbers from least to greatest: 1, 12, 15, 65, 765, 890

Since there is an even number of numbers, find the average of the middle two numbers.

15 + 65 = 80
80 ÷ 2 = 40
40 is the median

Mode   The mode of a set of numbers is the number that appears most frequently in that set.

Example

What is the mode of the following set of numbers?

12, 14, 15, 15, 15, 17, 18

The number 15 appears most often in this set, so it is the mode of the set.

### Graphs

Often it is helpful to represent numbers in a visual form called a graph. The most common types of graphs are circle graphs, bar graphs, and line graphs. You probably won't be asked to construct such graphs on the ASVAB, but you are likely to have to interpret one or more of them on the math and/or science sections of the test.

Types of Graphs   Some of the most common types of graphs are circle graphs, bar graphs, and line graphs.

Circle Graph This kind of graph uses a circle divided into parts to show fractional or percentage relationships.

Example

In a survey at a local high school, students were asked to name their favorite lunch food. The results of that survey are shown in the circle graph below.

Questions such as the following are typical.

• Which food was most (or least) popular with the students? (Most: sandwich; least: salad)
• Which two food selections of the students make up 50% of the total? (Sandwich and pasta: 40% and 10% = 50%)
• What is the ratio of the students who selected sandwiches to the students who selected hamburgers? (4:3)
• If the total number of students surveyed was 2,500, how many chose salad as their favorite lunch? (125; 2,500 × 0.05 = 125)

Bar Graph This kind of graph uses bars to provide a visual comparison of different quantities.

Example

The following bar graph compares the number of different types of sandwiches sold on Monday at a certain sandwich shop.

Questions such as the following are typical.

• Which kind of sandwich did the store sell the most of on Monday? (Turkey)
• How many more turkey sandwiches than egg salad sandwiches were sold on Monday? (8)
• How many tuna sandwiches and cheeses sandwiches were sold on Monday? (13)

Line Graph This kind of graph is generally used to show change over time.

Example

The following line graph shows the change in attendance at this year's football games.

Questions such as the following are typical.

• How many more people attended game 2 than game 1? (2,000)
• Which game had the highest attendance? (Game 7)
• How many people attended the last game of the year? (6,000)