How to find the average with examples
How do you find the average?
In mathematics, what people usually refer to as the average is known as the "mean" or "average number." There are two types of averages: the "mode" and the "median," which you learn about when studying statistics. However, in most mathematical applications, the term average refers to finding the mean, which can be calculated with addition and division.
To calculate the average, sum all the data and divide by the number of data you have added. The result is the average.
How and why do we calculate averages?
What does it mean to calculate an average?
Technically, you divide the sum of the values you are working on by the number of data in that set.
But in real-world terms, it's similar to distributing the values of the entire set evenly across each number, then going back and checking the values where the numbers became all the values.
This type of average can help you understand the meaning of a big data set or estimate the position of an entire group. For example, you may be asked to calculate the average grade for a class, the average salary for a particular job, the average time it takes to walk to the bus stop, the average GPA of your students, etc.
What about other types of averages?
If you list all the numbers in a data set from the smallest to largest, the mode is the value repeated most often, and the median is the middle value in that list.
Examples of calculating averages
Does the idea of how to find the average make sense to you?
Formulas are a bit clunky to write in words, but working with a few examples will help you get the concept.
Example 1. Find the average grade in a math class.
There are 12 students and their cumulative percentage grades are 76, 60, 89, 95, 84, 74, 82, 93, 79, 80, 81, 90.
Start by adding up all the students' scores.
76 + 60 + 89 + 95 + 84 + 74 + 82 + 93 + 79 + 80, 81, 82 = 821
Next, divide that total by the number of scores you added.
975 / 12 = 82.25
The resulting score of 82.25 is the average score for the math class.
Example 2. Find the average of 3, 2, 4, 6, 9, 21, 13, 5, 12, and 8?
Start by adding them all together.
3 + 2 + 4 + 6 + 9 + 21 + 13 + 5 + 12 + 8 = 83
Next, you count up the total number. Since there are 10, the next step is to divide the total (83) by 10.
83 / 10 = 8.3
Thus, the average for that data set is 8.3.
Example 3. Find the average walking time
Seven of the students in a class take the bus to school. These seven students are in and out of the bus for a total of 90 minutes each day. What is the average walking time of the students in your class?
Usually, the first step to do is to add all the walking time of all the students. However, that has already been done. The total walking time is 90 minutes.
This problem also indicates the number of data we are processing, 7 (7 students). Therefore, if you read carefully, all that is left to do to find the average is divide the total walking time (90 minutes) by the number of students (7).
90 minutes divided by 7 = 12.85714 minutes
Most people do not care whether you walked 12.85714 minutes. Therefore, in such cases, we almost always round the answer to make it more useful.
If rounding is allowed, the teacher will tell you whether or not to round to the nearest whole number. In this case, round to the nearest tenth, which is one spot to the right of the decimal. Thus, the rounded value is 12.9 minutes.