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Chapter 13: Problem 53

Find the arithmetic mean for each set of values. $$ 8,11,14,9,7,6,8 $$

Short Answer

Expert verified
The arithmetic mean is 9.

Step by step solution

01

Sum the Values

Add all the numbers in the set together: \[ 8 + 11 + 14 + 9 + 7 + 6 + 8 = 63 \]
02

Count the Number of Values

Determine how many numbers are in the set. There are 7 numbers in the set: \[ 8, 11, 14, 9, 7, 6, 8 \]
03

Divide the Sum by the Number of Values

Divide the sum obtained in Step 1 by the number of values counted in Step 2 to find the arithmetic mean: \[ \frac{63}{7} = 9 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

sum of values
To find the arithmetic mean, the first step is to sum all the values in the given set. This essentially means adding all the numbers together. For example, if we have values \[ 8, 11, 14, 9, 7, 6, 8 \], we need to add them like this:
\[ 8 + 11 + 14 + 9 + 7 + 6 + 8 \]
The result of this addition is \[ 63 \]. The sum is the total value you get after combining all the numbers.
number of values
Next, we need to determine how many numbers there are in the set. This step is crucial because it tells us how many parts we are dividing the total sum into.
For the set \[ 8, 11, 14, 9, 7, 6, 8 \], we count each number: \[ 1, 2, 3, 4, 5, 6, 7 \].
So, there are 7 numbers in total. This count helps us in the final step to distribute the total sum evenly.
division
The final step to find the arithmetic mean is division. We take the sum we calculated in the first step and divide it by the number of values we counted in the second step.
Using our example, the sum is \[ 63 \] and the number of values is \[ 7 \].
So, we perform the division:
\[ \frac{63}{7} \].
Performing this division, we get \[ 9 \]. This is our arithmetic mean. This step ensures that the total sum is evenly distributed across all values, giving us the average.

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