[Maths Class Notes] on Average Pdf for Exam

• The mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set is known as average.

• Average has many applications in real-life.

• Suppose we need to find the average age of men or women in a village or average female height in India. We can calculate it by adding all the values and dividing it by the number of values we have added. 

• Here’s the average formula in math that evaluates the average = [frac{text{sum of elements}}{text{number of elements}}]

 

Average

Finding an average of the data lets you find the estimate of a set of the data which is why the average is always between the highest and the lowest value of the data set. 

It is calculated by adding the values of a data set and then dividing it by the total number of items as given in the data set. 

Average Symbol:

• The average can basically be defined as the mean of the values which are represented by x̄ (x bar) also known as the average symbol.

• The average symbol can be denoted by ‘μ’.

 

Average Formula in Maths:

The formula that will tell you how to calculate the average of a list of numbers or values is very simple in Mathematics.

 

Here are the steps that will tell you how to calculate the average:

Step 1) Firstly, you need to add all the numbers given in the list 

Step 2) Then divide the calculated sum by the number of terms given in the list.

Step 3) The average of numbers can be expressed as:

[text{Average} = frac{text{sum of Values of the list }}{text{Total Number of values in a list}}] 

 

Here’s an average example for better understanding,

Given a set of values: 1, 2, 3, 4, and 5.

We know that 

[text{Average} = frac{text{sum of Values of the list }}{text{Total Number of values in a list}}] 

 

Step 1) Sum of the numbers (1+2+3+4+5) = 15

Step 2) Total number of terms = 5, divide the sum by the total number of terms,

Putting the sum and the number of terms in the formula that we know from the definition of average,

[text{Average} = frac{text{sum of Values of the list }}{text{Total Number of values in a list}}] 

[text{Average} = frac{15}{5} = 3]

 

What is the Average of Negative Numbers?

If there are negative numbers present in the list of numbers, even then the process or formula to calculate the average remains the same. 

 

[text{Average of negative numbers} = frac{text{sum of the terms}}{text{number of terms}}] 

 

Let’s understand the concept of an average of negative numbers with an example.

 

Average examples: Find the average of 4, −7, 5, 10, −1.

 

Solution. Lets’ first find the sum of the given numbers.

= 4 + (-7) + 5 + 10 + (-1)

= 4 – 7 + 5 + 10 – 1

= 11

Total number of terms = 5

As we know the formula to calculate the average from the definition of average,

[text{Average} = frac{text{sum of the terms}}{text{number of terms}}] 

[text{Average} = frac{11}{5} = 1.2]

           Average is equal to 1.2.

What is the Difference Between Mean and Average?

Here’s the main difference between mean and average:

Difference Between Mean and Average

 

 

Questions to be Solved (Average Examples):

Question 1) Find the average of the first five even numbers.

Solution) In Mathematics, the first five even numbers are as follows: 2, 4, 6, 8, 10

Now, we will add these numbers = 2 + 4 + 6 + 8 + 10 = 30

Total number of terms = 5

As we know the formula to calculate the average,

[text{Average of negative numbers} = frac{text{sum of the terms}}{text{number of terms}}] 

[text{Average} = frac{30}{5} = 6]

The average is equal to 6.

 

Question 2) Find the average of the given numbers, 6, 13, 17, 21, 23.

Solution) Let’s add the given numbers = 6 + 13 + 17 + 21 + 23 is equal to 80.

Total number of terms = 5

 

As we know the formula to calculate the average,

 

[text{Average of negative numbers} = frac{text{sum of the terms}}{text{number of terms}}] 

[text{Average} = frac{80}{5} = 16]

 

The average is equal to 16.

 

Question 3) If the ages of 10 students in a football team are 12, 13, 11, 12, 13, 12, 11, 12, 12, and 2, respectively, then find the average age of the students in the football team.

Solution) Given ages of students are 12, 13, 11, 12, 13, 12, 11, 12, 12, and 2.

Let’s find the sum of the ages of students.

Sum = (12 + 13 + 11 + 12 + 13 + 12 + 11 + 12 + 12 + 2) = 120

Total number of terms = 10

As we know the formula to calculate the average,

[text{Average of negative numbers} = frac{text{sum of the age of the students in the football team}}{text{total number of students}}] 

[text{Average} = frac{120}{10}]

The average age of the students of the football team is equal to 12.

 

Question 4) If the heights of females in a class are 5.5, 5.3, 5.7, 4.9, 6, 5.1, 5.8, 5.6, 5.4, and 6, then find the average height of females of the class.

 

                                           ()

 

Solution) Given heights of females = 5.5, 5.3, 5.7, 5.9, 6, 5.1, 5.8, 5.6, 5.4, 6

Sum = (5.5 + 5.3 + 5.7 + 4.9 + 6 + 5.1 + 5.8 + 5.6 + 5.4 + 6) = 56.3

Total number of terms = 10

As we know the formula to calculate the average,

[text{Average of negative numbers} = frac{text{sum of the Heights of Females}}{text{total number of females}}] 

[text{Average} = frac{56.3}{10}]

The average height of the females in the class is 5.63.