Question

If the means of two distributions are M₁ and M₂, while their respective frequencies are f₁ and f₂, then the combined mean of the two distributions will be
1. \(\frac{{{M_1} + {M_2}}}{{{f_1} + {f_2}}}\)
2. \(\frac{{{M_1}{f_1} + {M_2}{f_2}}}{{{f_1} + {f_2}}}\)
3. \(\frac{{{M_1}{f_1} + {M_2}{f_2}}}{{{M_1} + {M_2}}}\)
4. None of the above

Answer 1

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

\(\Rightarrow \frac{{{M_1}{f_1} + {M_2}{f_2}}}{{{f_1} + {f_2}}}\)

\(Combined\ mean\ of\ two\ distributions\ is\ {M_1 f_1 + M_2 f_2 \over f_1 + f_2}\)