Basics of average for shortcut trick

Introduction

These are the important points to be remembered while solving problems smartly .By using these points we can solve the average problem quickly in easy way. An average is the sum of a group of values divided by ‘n’, where ‘n’ is the total  number of values in the group. This can shown as

 

Average = sum of values / total number of values

An average is also known as mean or it can also be called as arithmetic mean or it can also be said as an equal distribution of values. 

  Basics of shortcut trick

1.If all the given quantities have the same value, then the number itself is the average.

    eg: Find the average of

    11   11    11   11   11  

    average =11

    [This point indirectly says that average is equal distribution of values]

2.If all the given quantities are not same ,then the average of the given quantities is always greater than the smallest number and always less than the largest number.

     S< avg< L

     Eg: find the average of

     14, 18,15, 25, 20

     Smallest no- 14     

                           average=18.4

     Largest  no- 25 

   3.If each of the given quantities is increased by a constant P ,then their average is also increased by P and vice –versa.

    Eg: The average of 6 number is 26.If each of the given number is increased by 4,then new average is?  

      =26 +4=30

      suppose if it is decreased 

      answer will be      

      = 26-4=22

4.If each of the given quantities is multiplied by a constant P ,then their average is also multiplied by P.

   Eg: The average of 24 number is 18.if each item of the series is multiplied by 3, the new average is?

     =18*3=54

5. If  the given quantities are in the form of arithmetic sequence, then average is considered as middle term of the given sequence.

      Eg: Find the average of

      5,  7,  9,  11,  13

      This question is in arithmetic sequence and middle term is 9 therefore average is 9.