The arithmetic mean of 10 observations is 48. If two more observations 65 and 75 are added to the data. then the arithmetic mean of the entire data of 12 observations is:

The mean of 10 observation is 48

Likewise the mean if the two added observation is 70(65+75/2=70)

Using Alligation method:

Step 1: 10           2

            48          70

                    ?

Step 2: 48          70

                  ?

            5     :     1

Step 3: 5+1=22

            1=11/3

so as 1=11/3,so 5=55/3

putting those values we get ,

Step4:   48       70

                   ?

             55/3     :    11/3

Step 5:   48           70

                  155/3 OR 15 2/3

             55/3       11/3