Average for Fifth Grade

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Average for Fifth Grade

What is the average?

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 third grade B students, in reality, we are asking what is the height that 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.

How is the average calculated?

  1. First step
    All the given values are added up.
  2. Second step
    The result is divided by the total number of addends to arrive at the average.
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Calculate the average of

\( 10 \), \( 10 \), \( 10 \), and \( 10 \).

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Average for Fifth Grade

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?


What is the average?

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 3rd 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.


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How is the average calculated?

  1. First step
    All the given values are added up.
  2. Second step
    The result is divided by the total number of addends to arrive at the average.

Let's look at an example

The grade that Diana got in math is 6767, in English 8585 and in language 4040.
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=19240+85+67=192

Then:
We will divide the result by the total number of addends.
In this exercise, we have been given 33 grades, therefore, we will divide 192192 by 33.
We will obtain:
192:3=64192:3=64
Diana's average grade is 6464.


Do you know what the answer is?

Another example:

Laura collected 55 flowers, Daniel 66 flowers, Betina 22, Ben 22 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=155+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 00 for Gaia's flowers. The 00 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 - 55 addends.

We will obtain:
15:5=315:5=3
The average number of flowers collected by the children is 33.
Note:
It is interesting to observe that the average describes a hypothetical situation in which, if each of the children had collected 33 flowers, we would have arrived at the same total amount -> 1515.


Particularities of the Average Worth Knowing

Let's take the group of numbers 3030, 1212 and 1515.
Let's calculate their average to understand several impressive characteristics about this topic.
15+12+30=5715+12+30=57
57:3=1957:3=19
The average of the group of numbers 1515, 1212, 3030 is 1919.

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 1919, the average will not be affected.
Let's see:
15+12+30+19=7615+12+30+19=76
76:4=1976:4=19  The average remains 1919.

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 – 1919, it will increase.
Let's see:
Let's add the number 2525, which is greater than 1919.
15+12+30+25=8215+12+30+25=82
82:4=20.582:4=20.5
Indeed, the average has increased from 1919 to 20.520.5

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 1919, it will decrease.

Let's see:
Let's add the number 1010, which is smaller than 1919.
15+12+30+10=6715+12+30+10=67
67:4=16.7567:4=16.75
Indeed, the average has decreased from 1919 to 16.7516.75

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 22, the average will increase by 22 the fixed number we have added.
Let's see:
15+2=1715+2=17
12+2=1412+2=14
​​​​​​​30+2=32​​​​​​​30+2=32
The new group of numbers is 17,14,3217,14,32
17+14+32=6317+14+32=63
63:3=2163:3=21
Indeed, the average has also increased by 22, from 1919 to 2121.

The average does not necessarily have to appear among the numbers given in the group
As we have seen, the average 1919 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.


Examples and exercises with solutions on average for fifth grade

Exercise #1

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

Video Solution

Step-by-Step Solution

Let's solve this problem step-by-step:

  • Step 1: Count the balls.
    In the provided diagram, we need to count each ball shown to obtain the total number.
  • Step 2: Determine the number of columns.
    The table's columns are evenly spaced, and there appears to be 4 columns depicted.
  • Step 3: Calculate the number of balls per column.
    Divide the total number of balls by the number of columns.

Step 1: Count the balls.

There are 20 balls depicted in the diagram.

Step 2: Determine the number of columns.

There are 4 columns in the table based on the grid lines visible in the diagram.

Step 3: Perform the division.

The formula to find the number of balls per column is: total number of ballsnumber of columns=204=5\frac{\text{total number of balls}}{\text{number of columns}} = \frac{20}{4} = 5.

Thus, there will be 5 balls in each column.

Answer

5

Exercise #2

If the balls below are divided so that each column in the table contains an equal number, then how many balls will each column contain?

Video Solution

Step-by-Step Solution

Let's work through these steps:
Step 1: Count the balls. We have a total of 12 balls displayed in the image.
Step 2: Count the columns. There are 4 columns shown in the SVG.
Step 3: Divide the total number of balls (12) by the number of columns (4).

Performing the division yields: 124=3 \frac{12}{4} = 3

Therefore, each column will contain 3 balls.

Answer

3

Exercise #3

Calculate the average

of 20 20 , 0 0 , and 7 7 .

Video Solution

Step-by-Step Solution

The average of a set of numbers is found by dividing the sum of the numbers by how many numbers there are.

Let's find the average of the numbers 2020, 00, and 77:

  • Step 1: Calculate the sum of the numbers:
    20+0+7=2720 + 0 + 7 = 27.
  • Step 2: Count how many numbers there are. Here, we have 3 numbers.
  • Step 3: Apply the average formula:
    Average=273\text{Average} = \frac{27}{3}.
  • Step 4: Divide the sum by 3:
    273=9 \frac{27}{3} = 9.

Therefore, the average of 20, 0, and 7 is 99.

Answer

9

Exercise #4

Calculate the average of 20 20 and 10 10 .

Video Solution

Step-by-Step Solution

To calculate the average of the numbers 20 and 10, we will follow these steps:

  • Step 1: Add the two numbers together. We have 20+10=30 20 + 10 = 30 .
  • Step 2: Divide the sum by the number of values, which is 2. So, we have 302=15 \frac{30}{2} = 15 .

Therefore, the average of 20 and 10 is 15 15 .

Answer

15

Exercise #5

Calculate the average of

2 2 , 6 6 , 8 8 , and 4 4 .

Video Solution

Step-by-Step Solution

To calculate the average of the numbers 2, 6, 8, and 4, we will follow these steps:

  • Step 1: Calculate the sum of the numbers.
  • The numbers given are 22, 66, 88, and 44. Therefore, we find the sum as follows:

    2+6+8+4=202 + 6 + 8 + 4 = 20.

  • Step 2: Count the number of numbers.
  • We have a total of 4 numbers.

  • Step 3: Calculate the average by dividing the sum by the count.
  • The average is calculated by dividing the total sum by the count of the numbers:

    Average=204=5 \text{Average} = \frac{20}{4} = 5 .

Thus, the average of the numbers 22, 66, 88, and 44 is 5\boxed{5}.

Answer

5

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