###
**Questions on Average are asked in SBI
PO, IBPS, SSC CGL and all other competitive exams which makes it a crucial topic.
Read on to find out what is average along with the average formula.**

‘Averages’ a
topic we all studied in school and always been on the question paper of all
competitive exams like SBI PO, IBPS and SSC Exams. Though the topic is simple,
the questions on averages asked in these exams are definitely not simple. So
let’s start right from the basic by discussing what is average and them some
problems based on the average formula and then move higher up the ladder by
discussing problems of higher difficulty.

In this post
we will discuss the principal idea of what is average, the different approached
to the average formula and how the same average formula can be used to solve
different kind of problems in the regular way and in the smart way.

###
**What is Average?**

Average is a
standard mathematical operation that usually entails finding the central value
from amongst a group of values. It is also described as equal distribution of
the given amount among the group. Defined in mathematical terms it is the
numerical result obtained by dividing sum of two or more quantities by the
number of quantities. There is a regular average formula which can be adapted
to solve most problems on average.

Let us use
an example to discuss what is average? Sachin Tendulkar has an average of 44.83
in One Day International matches. We know that in lots of matched has scored over
100 runs and in a few he has even got out on zero! But his average is neither
of these extremes; in the 463 matches that he has played he has scored runs on
an average of 44.83 in each match.

###
**The Average Formula**

We just
discussed how Sachin Tendulkar has a One Day International Average of 44.83.

Sachin
Tendulkar has scored a total of 18,426 runs in 463 matches, so we can find out what
is the average -

Total Number
of Runs Scored/ Total No. of Matches Played

18426 / 463
= 44.83

How did we
reach this value? Is there an average formula that that helps us to find out
what is the average of the given data? Well yes! There is an average formula
that helps us find the average.

**here is a variable of a given set of people of entities. The only catch here is that all variables should be in the same unit.**

*Element*###
**An Example to Understand What is
Average and the Average Formula**

Let us look
at a question that will help you understand what is average -

Question:
There are 4 people- A, B, C and D. Each of them has Rs.70, Rs.60, Rs.30 and Rs.40
respectively. What is average sum of money between these 4 people?

Solution: As
per the average formula we know that average is nothing but the sum of all the elements
divided by the total number of elements. In this case, element is the amount that
each of these 4 people possess – 70, 60, 30 and 40.

So substituting
values in the average formula we get -

Average = (70
+ 60 + 30 + 40) / 4

Average =
Rs.50

Therefore we
can say, the average amount which each of these 4 people is Rs.50/-

*Element can be any variable like – weight, time, length, age, distance or speed. Average can be calculated for any variable but all the variables should be of the same type. Average cannot be calculated when different elements represent variables.*
Let’s say
the above question was slightly different, you were told that the average money
possessed by 4 people is Rs.50/-. Then what is the total sum of the money with
the 4 people together?

So now in
this case, total money is = Average Money x Total No. of People

Total Money
= 50 x 4 = 200

###
**Why is Average Important? **

Always remember
that the basic idea behind average is equitable distribution because average is
nothing but the equal distribution of the total value. In the above example we know
that there are 4 people and if you collect 70, 60, 30 and 40 from A, B, C and D
respectively, the total amount that you will have will be Rs.200/- And if you
divide this 200 amongst these 4 people, each of them will get Rs.50/-

###
**Why Happens When a Value is Added to
the Group of Values? **

A lot of
problems on average are about a new element being added to the group and you
have to find out its effect on the average value of the group. Now in this case
there are only 3 possibilities-

1) If the
value added to the group is equal to the average,

Let us
assume that another person ‘E’ joins the group and he has Rs. 50/- with him,
this amount is already equal to the average of the group, so you don’t need to
use the average formula all over again the new average, it will remain unchanged.

2) If the
value added to the group is more than the average,

Let us
assume that the other person ‘E’ who joins the group has Rs. 60/- This 10 more
than the average of the group. So to find the average rather than using the
average formula all over again, you can simply divide the difference by the
number of elements and add the value to the group to get the new average.

Here, it is
= (60 – 50) / 5 = 10/5 = 2

Therefore, we
add 2 to the old average and get the new average,

New Average
= 50 + 2 = 52

3) If the
value added to the group is less than the average, in that case the average
will decrease.

Let us
assume that the other person ‘E’ who joins the group has Rs. 40/- This 10 less
than the average of the group. So to find the average rather than using the
average formula all over again, you can simply divide the difference by the
number of elements and subtract the value to the group to get the new average.

Here, it is
= (50 – 40) / 5 = 10/5 = 2

Therefore, we
add 2 to the old average and get the new average,

New Average
= 50 - 2 = 52

###
**Practice Questions Using the Average
Formula**

Solve the
following questions using the average formula and do leave your answers in the
comments sections below!

Question 1.
What is the average of the following set of numbers? 302, 152, 132, 122, 112

1) 184 2) 165 3) 152 4) 176 5) None of these

Question 2.
Find the average of the following sets of scores. 198, 309, 256, 488, 145, 326,
427

1) 307 2) 10132 3) 11320 4) 11230 5) None of these

Stay Tuned for the next post in the series
where we discuss the different kinds of questions asked from Average in SBI PO,
IBPS and SSC Exams.

And remember
to never stop practicing!

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