Arithmetic Mean

Arithmetic mean

Test paperProblem: 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:

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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.


Drivers on roadExample 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

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Answer: The mean driving speed is 62.5 mph.


Gas pumpExample 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

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Answer: The mean gasoline price is $1.86.


MarathonExample 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

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Answer: The mean race time is 4.9 hr


PoolExample 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

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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.

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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
ANSWER BOX:   

RESULTS BOX: 

2. Find the mean of the decimals listed below.
5.3,  5.5,  2.2,  4.8,  3.2
ANSWER BOX:   

RESULTS BOX: 

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
ANSWER BOX:   

RESULTS BOX: 

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
ANSWER BOX:  $   

RESULTS BOX: 

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

RESULTS BOX: