Tuesday, 25 April 2017

Averages I- What is Average and the Average Formula for IBPS PO Exam

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

Average Formula
‘Averages’ a topic we all studied in school and always been on the question paper of all competitive exams like  IBPS PO 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.
Average Formula
Average Formula
Element 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.

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/-
Average Formula 

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,
Average Formula
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,
Average Formula
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.
Average Formula
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
Average Formula

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 IBPS PO Exams.


And remember to never stop practicing! 
Average Formula

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