Like its, name in this method we assume a number as the mean of the given data. Then we subtract this assumed mean from all class marks. Hence find d_{i}. Let a is our assumed mean and x_{1}, x_{2}, x_{3} .......x_{n} are the class marks. Then
d_{1} = x_{1}  a d_{2} = x_{2}  a d_{3} = x_{3}  a


d_{n} = x_{n}  a
Collectively we can write d_{i} = x_{i}  a After that we calculate f_{i} d_{i} = f_{1} d_{1} + f_{2} d_{2} + f_{3} d_{3} +  + f_{n} d_{n} Now Since d_{i }= x_{i}  a Therefore This is the formula for calculating mean with assumed mean method. The method will be more clear with following example Note : You can assume any number as assumed mean (a) but the general choice is any x_{i} which lies in the middle of range of x_{i}. Example: Calculate the mean of following data with the help of assumed mean method. C. I  10  20  20  30  30  40  40  50  50  60  60  70  70  80  80  90  90  100  100  110  f_{i}  4  5  4  4  3  4  16  13  11  16  Solution: C . I .  x_{i}  f_{i }  d = x_{i}  a  f_{i}d_{i }  10 20  15  4  40  160  20 30  25  5  30  150  30  40  35  4  20  80  40  50  45  4  10  40  50  60  55 ← a  3  0  0  60 70  65  4  10  40  70 80  75  16  20  320  80 90  85  13  30  390  90  100  95  11  40  440  100  110  105  16  50  800    f_{i} = 80   f_{i} d_{i} = 1560  Let a = 55 Now = 55 + (1560 / 80) = 55 + 19.5 = 74.5
