# Arithmetic Mean

Problem: Scott took 7 math tests in one marking period. What is the mean test score?

89, 73, 84, 91, 87, 77, 94

Solution: The sum of these numbers is 595. Dividing the sum by the number of test scores we get:

Answer: The mean test score is 85.

**Definition: **The **arithmetic mean** of a set of data is found by taking the sum of the data, and then dividing the sum by the total number of values in the set. A mean is commonly referred to as an average.

In the problem above, the mean was a whole number. This is not always the case. Let’s look at some more examples.

Example 1: Find the mean driving speed for 6 different cars on the same highway.

66 mph, 57 mph, 71 mph, 54 mph, 69 mph, 58 mph

Solution: 66 + 57 + 71 + 54 + 69 + 58 = 375

Answer: The mean driving speed is 62.5 mph.

Example 2: The Scheuern family drove through 4 midwestern states on their summer vacation. Gasoline prices varied from state to state. What is the mean gasoline price?

$1.79, $1.61, $1.96, $2.08

Solution: $1.79 + $1.61 + $1.96 + $2.08 = $7.44

Answer: The mean gasoline price is $1.86.

Example 3: A marathon race was completed by 5 participants in the times given below. What is the mean race time for this marathon?

2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr

Solution: 2.7 + 8.3 + 3.5 + 5.1 + 4.9 = 24.5

Answer: The mean race time is 4.9 hr

Example 4: Find the mean swimming time rounded to the nearest tenth:

2.6 min, 7.2 min, 3.5 min, 9.8 min, 2.5 min

Solution: 2.6 + 7.2 + 3.5 + 9.8 + 2.5 = 25.6

Answer: The mean swimming time to the nearest tenth is 5.1 min.

**Summary:** The **arithmetic mean** of a set of n numbers is the sum of the n numbers divided by n. The mean is commonly referred to as an average.

**Exercises**

Directions: Find the mean of each set of data. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. |
Find the mean of the whole numbers listed below.1, 8, 7, 6, 8, 3, 2, 5, 4, 5 |

2. |
Find the mean of the decimals listed below.5.3, 5.5, 2.2, 4.8, 3.2 |

3. |
Find the mean rounded to the nearest tenth.0.34, 0.12, 0.48, 0.56, 0.71, 0.8, 0.65, 0.82 |

4. |
Employees at a retail store are paid the hourly wages listed below. What is the mean hourly wage?$7.50, $9.25, $8.75, $9.50, $7.25, $8.75 |

5. |
What is the mean test score?83, 71, 91, 79, 87, 80, 95, 79, 91, 85, 94, 73 |