In math, a mean represents the average value of a certain set of values. We often use the term mean interchangeably with average, but we need to make a clear distinction. The term average should only be used interchangeably with the arithmetic mean. It is calculated by dividing the sum of all values, with the number of values in a given set. This is the one we are most familiar with, because it is the most often used. The two lesser used means are the geometric mean and the harmonic mean.
The arithmetic mean is used for absolute values, such as per capita income, which is the average income of a person in a certain area. It is, however, not a perfect solution, as outliers can skew the result, and give you the wrong picture of the situation. In those situations, it is better to use the median.
The geometric mean, unlike the arithmetic means, is used for calculating growth rates. This is because growth rates are expressed as percentages and not absolute values. Because of this, it is most often used in business and finance for calculating things such as portfolio returns and stock indexes.
The harmonic mean, because of its seemingly weird formula, is used when dealing with fractions. You can calculate the relationships between fractions without having to worry about common denominators. It is also used to identify some patterns, such as the Fibonacci sequence.
How to calculate the mean: Practice questions
As we said, calculating the arithmetic mean is very simple. You just need to add up all the values in a set, and divide the result by the number of values in that set. We’re going to do some examples here.
Let’s say 5 people compete in a race. After the race is finished, the standings are as follows:
- 78 seconds
- 79 seconds
- 81 seconds
- 83 seconds
- 86 seconds
What would the average time of completion for the race be? Let’s do the first part, which is deciding what mean we should use. Since the standings are absolute values, we are going to use the arithmetic mean. Now, we need to add up all the numbers. Once we do, we see their sum is 407. Now, we need to divide by the number of racers, which is 5. Once we do that, we see that the arithmetic mean of those 5 numbers, or the average time of completion for the race is 81.4 seconds.
For our second example, let’s look at the grading system most schools in the world use. When it comes to calculating the final grade of the first semester, for any subject, and any student, the arithmetic mean of all their grades, from that subject, is used. The grades range from 1 to 5, with 1 being the worst, and 5 being the best.
Let’s say a student, at the end of their first semester, had the following grades from biology: 5, 5, 5, 3, 4. What would his final grade for biology be, at the end of the first semester? Let’s go through the process again. First, we add up all the grades this student had. Once we do, we see their sum is 22. Now, we need to divide that sum by the number of grades they had, which is 5. Once we divide, we see that the final grade would be 4.4, which ultimately rounds down to a 4.
How to find the mean with the mean calculator
Of course, why go through the trouble of calculating everything manually, when you can use our mean calculator, and be done in no time. With the mean calculator, you simply need to input the values, and the calculator will calculate not just the arithmetic mean, but the geometric and harmonic means as well. This can especially be useful when dealing with the latter two means, as they require more complex mathematical operations, such as exponentiation and roots. For more information about this subject, and our mean calculator, you can visit.
Laila Azzahra is a professional writer and blogger that loves to write about technology, business, entertainment, science, and health.