91Ó°ÊÓ

Finding the arithmetic mean, also known simply as the mean or average, is a common task in mathematics that helps us understand the central tendency of a set of numbers. When you are asked to find the mean, you are essentially finding the balance point of the numbers in the set. The arithmetic mean is calculated by taking the sum of all the numbers and then dividing this sum by the count of numbers in the set. This gives us a single value that represents the average of those numbers.
Let's dive into an example:
Consider the set of numbers: \(105,114,123,101,100,111\). The mean of this set needs to be found. We follow the steps of summing up the numbers and then dividing the sum by the number of values.

The first step in finding the arithmetic mean is to compute the sum of all the numbers in your set. This is a straightforward process where you simply add all the numbers together. In our example, we have the numbers \(105,114,123,101,100,111\).
Let's break down the addition:
\(105 + 114 = 219\)
\(219 + 123 = 342\)
\(342 + 101 = 443\)
\(443 + 100 = 543\)
\(543 + 111 = 654\)
So, the sum of these numbers is 654.
This sum will be used in the next step to find the mean.

Once you have the total sum of the numbers in your set, the next step is to divide this sum by the number of values. This step gives you the arithmetic mean. In our example, we already calculated the sum to be 654. We then count the total number of values in the set, which is 6.
The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of values}} \] Substituting the numbers we have:
\[ \text{Mean} = \frac{654}{6} \]
Now we simply perform the division:
\[ \frac{654}{6} = 109 \]
Therefore, the mean (average) of the set \(105,114,123,101,100,111\) is 109.
Understanding this process ensures that you can accurately find the mean for any set of numbers by following these simple steps.