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Average: Concept , Questions with examples and worksheet

In this article we are going to discuss about Average,you would often hear this term from people around you. folks generally say average temperature, average marks, average height, average salary etc.
Before we get into the definition of Average let's start with an example that will make you familiar with the concept in easier way.

what is average



Example 1 : Alex brings 5 identical balls of red colour for a total of  £50 ( Ball 1-  £12 , Ball 2 - £8 , Ball 3- £10 , Ball 4 - £17 ,Ball 5 - £13 ) and each of them has different price. when he reaches his home he forgets which ball corresponds to which price. His friend joy comes to him and asks for a ball. Now at what price should Alex sell one ball so that he makes no profit no loss ?

The problem above can be very easily solved if you have even a basic idea of Average. 

Alex payed £50 for 5 balls. 
Average Price for one Ball = £50/5
                                                = £10/Ball 

Alex should sell one ball for £10 .

Example 2 : Doe was asked to record temperature from Monday to Thursday But on Tuesday he was out of town, so couldn't record the temperature for that particular day. The temperature for other days Monday- 36°C, Wednesday- 37°C, Thursday- 34°C.
He wanted to know the approximate temperature for Tuesday So he calculated the average temperature for the 3 days which was 

       = 36+37+34
       = 107/3 

Average Temperature for one day  = 35.6 °C
So the approximate temperature on Tuesday could be 35.7°C

If the examples are clear to you let's dive into it .

What is average 

The mathematical expression to calculate the average is :

Average = Total sum of quantities/ Number                                                              of quantities 
Or 
Average = Total sum/Total Numbers 

Let's put the formula into examples to calculate the average.

Example 3 : The heights of 4 students are as follows 5 feet ,5 feet,6 feet and 8 feet.What is the average height? 

Sum of all students' height = 5 feet + 5 feet +                                                   = 6 feet + 8 feet. 
                                                 = 20 feet 
Number of students.    = 4

Average height = 20 feet/ 4
                            = 5 feet 

Example 4 : Temperature for a particular week was  recorded in London.the data for temperature from Monday to Sunday is as follows 21°c, 34°c,  30°c, 24°c, 29°c, 28°c , 26°c

Total sum of temperature = 21°c +34°c + 30°c                                                  +24°c + 29°c + 28°c                                                  + 26°c
                                              =  192°c

Total number of days for which the temperature was recorded = 7 

Average temperature = 192/7
                                      = 27.4 °c

How to calculate Weighted average

The Weighted average is generally given by the following formula 

If N1 ,N2 and N3 have average A1 ,A2 and A3 respectively then the Weighted average is:

Weighted average = (W1+W 2+W 3)/N1 +N2+N3

= (N1×A1 + N1×A1+ N1×A1)/N1+N2+N3

Let's take an example to explain it.

Consider average marks of 6 students out  from different classes. Average marks of Ena and joe from class 4 is 60 and Average marks of John and Ray is from class 6 is 44.Average marks of Carl and Lina from class 8 is 52. Find the Weighted average 


Sum of the marks of Ena and Joe = 2×60
                                                             =120

Sum of the marks of John and Ray 
= 2×44
=88

Sum of the marks of Carl and Lina 
= 2×52
=104

Weighted average of the marks of 6 students 
= (120+88+104)/6
= (312)/6
= 52

Example : In a tech company,There are two teams namely green team and red team.The average salary of all 5 workers working in the green team is 40 k and salary of red team workers is 50 k and the weighted average salary of all employees is 45 k find the number of employees in the Red team.

Ans : Let the number of workers in the Red team= x

Weighted average = (5×40+50×x)/(5+x)
                            45   = (200+50 x)/(5+x)

225 + 45 x = 200+50 x
5 x = 25
x = 5

Number of workers in red team = 5.


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