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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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?

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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

Below is a table describing the number of toys Jonathan has in his toy boxes.

Calculate the average number of toys in each box.

Toy BoxNumberofToys123372

Step-by-Step Solution

To solve this problem, we'll calculate the average number of toys in Jonathan's toy boxes using the following steps:

  • Step 1: Identify the total number of toys. Add up the quantities of toys from each box.
  • Step 2: Calculate the average by dividing the total number of toys by the number of boxes.

Let's perform the calculations:

Step 1: The number of toys in Box 1 is 3, in Box 2 is 7, and in Box 3 is 2. Therefore, the total number of toys is:

3+7+2=12 3 + 7 + 2 = 12

Step 2: There are 3 toy boxes. We calculate the average number of toys per box by dividing the total number of toys (12) by the number of boxes (3):

Average=123=4 \text{Average} = \frac{12}{3} = 4

Therefore, the average number of toys in each box is 4 4 .

Answer

4

Exercise #2

Below is a table describing the number of goals scored by Manchester United in each match during a season.

Calculate the average number of goals they scored per match.

MatchGoalsScored1234540562

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the total number of goals scored.
  • Step 2: Count the total number of matches played.
  • Step 3: Use the formula for average to find the average number of goals scored per match.

Now, let's work through each step:

Step 1: Calculate the total number of goals scored.
The goals scored in each match are: 44, 00, 55, 66, and 22.
The total number of goals scored is 4+0+5+6+2=174 + 0 + 5 + 6 + 2 = 17.

Step 2: Count the total number of matches played.
There are 5 matches in total.

Step 3: Use the formula for average.
The average number of goals per match is given by:

Average=Total number of goalsNumber of matches=175 \text{Average} = \frac{\text{Total number of goals}}{\text{Number of matches}} = \frac{17}{5}

Calculating the division:

175=3.4=325 \frac{17}{5} = 3.4 = 3\frac{2}{5}

Therefore, the average number of goals scored per match is 325 3\frac{2}{5} .

Answer

325 3\frac{2}{5}

Exercise #3

Below is a table describing how many marbles a group of children have.

On average, how many marbles does each child have?
NameNumberofMarblesBen276SarahFatimaVladimir1

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the number of marbles each child has from the table.
  • Step 2: Calculate the total number of marbles by adding all the individual counts.
  • Step 3: Determine the number of children in the group.
  • Step 4: Use the average formula to compute the average number of marbles per child.

Now, let's work through each step:

Step 1: Identify the number of marbles each child has.
From the table, we have the following information:
Ben has 2 marbles.
Sarah has 7 marbles.
Fatima has 6 marbles.
Vladimir has 1 marble.

Step 2: Calculate the total number of marbles.
Total marbles = 2+7+6+1=162 + 7 + 6 + 1 = 16

Step 3: Determine the number of children.
There are 4 children: Ben, Sarah, Fatima, and Vladimir.

Step 4: Use the average formula.
The average number of marbles per child is given by:
Average=164=4 \text{Average} = \frac{16}{4} = 4

Therefore, the average number of marbles per child is 44.

Answer

4

Exercise #4

What is the average number of teaspoons of sugar in each product?

Products'NameNumber ofSugar TeaspoonsCoke Can542ChocolateGumPopsicle3FriesBread SliceBerry322

Step-by-Step Solution

To find the average number of teaspoons of sugar per product, we follow these steps:

  • List the sugar content for each product: Coke Can (5), Chocolate (4), Gum (2), Popsicle (3), Fries (3), Bread Slice (2), Berry (2).
  • Sum the sugar content: 5+4+2+3+3+2+2=21 5 + 4 + 2 + 3 + 3 + 2 + 2 = 21 .
  • Count the number of products: There are 7 products.
  • Calculate the average using the formula Average=valuesnumber of values \text{Average} = \frac{\sum \text{values}}{\text{number of values}} .
  • Substitute the values into the formula: Average=217=3 \text{Average} = \frac{21}{7} = 3 .

Therefore, the average number of teaspoons of sugar in each product is 3 3 .

Answer

3

Exercise #5

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

Answer

5

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