The average (arithmetic mean or simply mean) is a simple and fun topic. In this article, we will learn what the average is, how to calculate it, and other peculiarities that are worth knowing about.

**Shall we start?**

The average is, in fact, a number that represents a group of numbers. It is the average, its center, therefore, it represents them.

When we ask, for example, what is the average height of the students in 3^{rd} grade B, we are actually asking what height would represent all of them.

It is true that each student has a different height, but the average collects the median measure of all the heights and results in a representative number of all of them.

The more short children there are in the grade the lower the average height will be, the more tall children there are in the grade it will be higher.

The grade that Diana got in math is $67$, in English $85$ and in language $40$.

What is Diana's average grade?

**Solution:**

We are looking for a single grade that represents all of Diana's grades! That is, the average (or mean). We will proceed according to the steps seen.

First, we will add all the grades :

$40+85+67=192$

**Then:**

We will divide the result by the total number of addends.

In this exercise, we have been given $3$ grades, therefore, we will divide $192$ by $3$.

**We will obtain**:

$192:3=64$

Diana's average grade is $64$.

Laura collected $5$ flowers, Daniel $6$ flowers, Betina $2$, Ben $2$ and Gaia none.

What is the average number of flowers collected by the children?

**Solution:**

We will proceed according to the steps, so first, we will add all the numbers together.

$5+6+2+2+0=15$

Now we will move to the second step and divide the result by the total number of addends.

Pay attention that we should also take into account the $0$ for Gaia's flowers. The $0$ enters into the average, as it also has to be reflected in the final result.

So we will add – Laura, Daniel, Betina, Ben, and Gaia - $5$ addends.

**We will obtain:**

$15:5=3$

The average number of flowers collected by the children is $3$.

**Note:**

It is interesting to observe that the average describes a hypothetical situation in which, if each of the children had collected $3$ flowers, we would have arrived at the same total amount -> $15$.

Let's take the group of numbers $30$, $12$ and $15$.

Let's calculate their average to understand several impressive characteristics about this topic.

$15+12+30=57$

$57:3=19$

The average of the group of numbers $15$, $12$, $30$ is $19$.

**Adding a number equal to the average does not change the average**

If we add to the group of numbers one that is equivalent to the average - in our example $19$, the average will not be affected.

Let's see:

$15+12+30+19=76$

$76:4=19$ The average remains $19$.

**Adding a number greater than the average will increase it**

If we add to the group of numbers one that is larger than the average - in our example – $19$, it will increase.

**Let's see:**

Let's add the number $25$, which is greater than $19$.

$15+12+30+25=82$

$82:4=20.5$

Indeed, the average has increased from $19$ to $20.5$

**Adding a number smaller than the average will decrease it**

If we add to the group of numbers one that is smaller than the average - in our example $19$, it will decrease.

**Let's see:**

Let's add the number $10$, which is smaller than $19$.

$15+12+30+10=67$

$67:4=16.75$

Indeed, the average has decreased from $19$ to $16.75$

**Adding a fixed number to every given number will increase the average according to the fixed number we have added**

If we add to each given number in the group of numbers any fixed number - for example $2$, the average will increase by $2$ the fixed number we have added.

**Let's see:**

$15+2=17$

$12+2=14$

$30+2=32$

The new group of numbers is $17,14,32$

$17+14+32=63$

$63:3=21$

Indeed, the average has also increased by $2$, from $19$ to $21$.

**The average does not necessarily have to appear among the numbers given in the group**

As we have seen, the average $19$ does not appear among the numbers of the group.

**The average can be a fraction instead of a whole number**

As we have seen in the previous example, the average could be a number that is not a whole number.