Correct Answer - Option 2 :
\(\frac{{{M_1}{f_1} + {M_2}{f_2}}}{{{f_1} + {f_2}}}\)
Concept
Mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by the number of observations in the data set.
Calculation
Mean M1 = Sum of first distribution/f1
⇒ Sum1 = M1f1
Similarly, Sum2 = M2f2
Combined mean = Total sum / sum of frequencies
\(\Rightarrow \frac{{{M_1}{f_1} + {M_2}{f_2}}}{{{f_1} + {f_2}}}\)
\(Combined\ mean\ of\ two\ distributions\ is\ {M_1 f_1 + M_2 f_2 \over f_1 + f_2}\)