Average Shortcut Methods

Rule 1: To find the Average


Total of all the quantities / Number of Quantities = Average

Example:
         
            If a man earns Rs. 40, Rs. 50 Rs.56, Rs.46 and Rs. 48 on 5 consecutive days of a week, Find
the average earnings per day?

Solution:
                  Total of all the quantities / Number of Quantities

                  = 40+50+56+46+48 / 5
                  = 240/5
                  = 48
Ans : Average earnings per day is 48

Rule 2: Average of different groups

Case :1

                                           No.of.quantities = m , Average = a

                                                               Sum = ma

                                           No.of.quantities = n, Average = b

                                                               Sum = nb

                                           Average of two groups added = ma+nb / m+n

                      Similarly, in

Case:2

                                          Average of remaining groups = ma-nb / m-n

Example:

                  The average age of students in section A of 40 students is 10 yrs and the average age of students in section B of 30 students is 12 years. Find average age of students in both section taken together?

Solution:

                     Average = ma+nb /m+n 

                                    = 40*10+30*12 / 40+30 

                                    = 760 / 70

                                    = 10.85 yrs

Rule:3           Change in the number of quantities and its effect on average

case:1

Sum of the quantities added =  [ change in no.of.quantities * original average] 
                                                                                + 
                                                     [change in average * final no.of.quantities]

Example :

                  The average weight of 29 students in a class is 48 kg. If the weight of the teacher is included, the average weight rises by 500g. Find the weight of the teacher?

Solution:

Here by above rule :3

                 change in no.of.quantites = 1
                 original average               = 48
                 change in average            = 0.5 (500g)
                 final no.of.quantities       = 30
                         
                    = (1*48) + (0.5*30)
                    = 63 kg

Case:2 


Sum of the quantities removed =  [ change in no.of.quantities * original average] 
                                                                                      -
                                                          [change in average * final no.of.quantities]

Example:

                   There are 50 boys in a class . Their average weight is 45kg. when one boy leaves the class, the average reduces by 100g. Find the weight of the boy who left the class

Solution

                change in no.of.quantites = 1

                 original average               = 45
                 change in average            = -0.1 (100g)
                 final no.of.quantities       = 49
               
                             = (1*45) - (-0.1*49)
                             = 45 + 4.9
                             = 49.9 kg