Quantitative Aptitude Average Tutorial (Study Material)

Quantitative Aptitude Average Tutorial  (Study Material)

The term average is used frequently in everyday life to express an amount that is typical for a group of people or things. For example, you may read in a newspaper that on average people watch 3 hours of  television per day. We understand from the use of the term average that not everybody  watches 3 hours of television each day, but that some watch more and some less. However , we realize from the use of the term average that the figure of 3 hours per day is a good indicator of the amount of TV watched in general.

 Quantitative Aptitude Average Tutorial (Download PDF)

Introduction

The idea of average is not new to us. We all are familiar with the following types of statements.
The average runs scored by Sachin Tendulkar in a series is 72.
The average marks secured by Kana is 78%.
If a man earns Rs 40. Rs 50. Rs 56. Rs 46 and Rs 48 on five consecutive days of a week, then he earns a total of Rs (40 + 50 + 56 + 46 + 48) = Rs 240.
To find his average earning per day, his total earning is divided by the number of days, i.e…
Average = 240/5 = Rs 48
Average earning does not mean that he earned Rs 48 everyday . But had he earned Rs 48 everyday, then his total earnings would have also been Rs 240 in 5 days.
Hence, to find the average of given quantities:
Step 1 The given quantities arc added to get a Sum
Step 2 The Sum is divided by the Number of items to get the Average.
Sum of all the items /Number of items = Average—- (1)
Note: The average is also called the Mean.
The quantities, whose average is to be determined, should he in the same unit.
Hence,  Sum of all the items = Average x no. of items        (2)

Average of Different Groups

Sometimes, the average of two different groups are known and the average of a third group (made by combining these two groups) is to be found out.

Let

Therefore, average of combined group = Sum of all Items/ No. of Items
A= ma+nb/m+n
This formula is also applicable for more than two groups forming the combined group.

Addition or Removal of Items and Change in Average

Since Average = Sum of Items / Number of Items

So, the original average may change (increase/decrease), if number of items change. The number of items may change in the following two cases,

Case I

When one or more than one New items are added
Let the average of N items = A
Now n New items are added and the average increases or decreases by x. then
Average of New items added = A ± (1+ N/n)
Use (-). when average decreases (+), when average increases.

Case II

When one or more than one items are removed

In this case, items arc removed, so on placing-N/n  in place of +N/n  in formula  it becomes.
Average of  items removed = A ± (1- N/n)
Use (-), when average decreases (+), when average increases
When only One item is removed, put n = 1, then
Value of the item removed = A ± (1 – N)x

Replacement of some of the Items

Sometimes, when a number of items of a group are removed and these arc replaced with equal number of different items, then the average of the group changes, (increases or decreases) by x.
Let there are N items in the group, then
Sum of New items added – Sum of removed items = ± Nx
Use (-). when average decreases (+), when average increases.

Example: When a man weighing 80 kg is replaced by anolher man in a group of five persons, the average weight decreases by 3 kg. What is the weight of new man?
Solution: Using formula (6).
Weight of new man – Weight of removed man = -Nx (-ve, average decrease)
Weight of new man – 80 = -5 x 3
Weight of new man = 80 – 15
= 65 kg.

Some Problem-Specific Formulae

Before t years, the average age of ‘Ar members of a family was *T” years. If the average remains same even after one more member joins the family, then present age of new member = T – Nt.
Example: Four years ago, the average age of six members of a family was 26 years. On the birth of a child in the family, the average remains the same. Find the present age of the child.
Solution: Present age of the child = 26-6 x 4 = 2 years.

Out of the given numbers, if the average of frst n numbers is x and that of last n numbers is y, then
First number – last number = n(x – y).

Example: The average temperature of June, July and August was 3I°C. The average temperature of July. August and September was 30 °C. If the temperature of June was 29 °C. find the temperature of September.
Solution: In the given problem, four months have been indicated, i.e.
June,   July,   August.   September
(first)      2              3              4 (last)
Out of these, the average temperature of first three (n = 3) months = 31°C°= x
and the average temperature of last three (n = 3) months = 30 °C = y Then, by the formula
Temperature of first month – temperature of last month = n(x – y)
temperature of June – temperature of September = 3(31 – 30).
29 – temp, of September = 3
Temperature of September = 26 °C

 Quantitative Aptitude Average Tutorial (Download PDF)