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Concept And Tricks On Average

What is Average

An average or more accurately an arithmetic mean is, in crude terms, the sum of n different data divided by n.

Averages of a group is defined as the ratio of sum of all the items in the group to the number of items in the group.

Average = (Sum of all items in the group)/ Number of items in the group

Now, sum of all items can be ‘the sum of number of quantities like apple, people etc’ or ‘sum of values of the item like 10 coins of 2Rs each etc’.

Some Important Concepts:

1. Average =total of data/No.of data

2. If the value of each item is increase by the same value a, then the average of the group or items will also increase by a.

3. If the value of each item is decreased by the same value a, then the average of the group of items will also decrease by a.

4. If the value of each item is multiplied by the same value a, then the average of the group or items will also get multiplied by a.

5. If the value of each item is multiplied by the same value a, then the average of the group or items will also get divided by a.

6. If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.

7.Average of n natural no's=(n+1)/2

8.Average of even No'=(n+1)

9.Average of odd No'= n

10.General Formula=(1st number +Last number)/2

Concept And Tricks Of Ratio And Proportion

What is Ratio?

A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a : b = a / b In ratio a : b , we can say that a as the first term or antecedent and b, the second term or consequent.

Example :  The ratio 4 : 9 we can represent as  4 / 9 after this 4 is a antecedent and , consequent = 9

Rule of ration :  In ratio multiplication or division of each and every term of a ratio by the same non- zero number does not affect the ratio.

Different type of ratio problem is given in Quantitative Aptitude which is a very essential topic in competitive exam. Under below given some more example for your better practice.

Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks and formula are comes into action.

What is Proportion?

The idea of proportions is that two ratio are equal.

If a : b = c : d, we write a : b : : c : d,

Ex. 3 / 15 = 1 / 5

a and d called extremes, where as b and c called mean terms.

Proportion of quantities

the four quantities a, b, c, d said proportion then we can express it

a : b = c : d

Then a : b : : c : d  <–> ( a x d ) = ( b x c )

product of means = product of extremes.

If there is given three quantities like a, b, c of same kind then then we can say it proportion of continued.

a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers.

So, b^2 = ac. ( middle number )^2 = ( First number x Last number ).