∴ Mean = The sum of all observations/Total number of observations
∴ The sum of all observations = Mean x
Total number of observations mean of nine numbers is 77
∴ sum of 9 numbers = 11 x 9 = 693 …(i)
If one more number is added, then mean increases by 5 mean of 10 numbers
= 77 + 5 = 82
∴ sum of the 10 numbers = 82 x 10 = 820 …(ii)
∴ Number added = sum of the 10 numbers – sum of the 9 numbers
= 820 – 693 … [From (i) and (ii)] = 127
∴ The number added in the data is 127.
