If `barx_1,barx_2,barx_3,...barx_n` are the means of n groups with `n_1,n_2,n_3,....n_n` numbers of observations respectively. Than the mean `barx` of all group together is given by :

Options

A. `sum_(i=1)^(n)n_(i)bar(x)_(i)`
B. `(sum_(i=1)^(n)n_(i)bar(x)_(i))/(n^(2))`
C. `(sum_(i=1)^(n)n_(i)bar(x)_(i))/(sum_(i=1)^(n)n_(i))`
D. `(sum_(i=1)^(n)n_(i)bar(x)_(i))/(2n)`

Explanation

To find the mean \( \bar{x} \) of all groups together, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Mean**:
The mean of a group is defined as the sum of all observations in that group divided by the number of observations in that group. For each group, we have:
\[
\bar{x}_i = \frac{\text{Sum of observations in group } i}{n_i}
...