For some data $x_{1}, x_{2}, \ldots x_{n}$ with respective frequencies $f_{1}, f_{2}, \ldots f_{n}$,

Question

For some data $x_{1}, x_{2}, \ldots x_{n}$ with respective frequencies $f_{1}, f_{2}, \ldots f_{n}$, the value of $\sum_{1}^{n} f_{i}\left(x_{i}-\bar{x}ight)$ is equal to:\

Professor PC Thomas Classes · Answer

(d): We know that, $\bar{x}=\frac{\sum_{i=1}^{n} f_{i} x_{i}}{\sum_{i=1}^{n} f_{i}}$\ $\Rightarrow \sum_{i=1}^{n} f_{i} \cdot \bar{x}=\sum_{i=1}^{n} f_{i} \cdot x_{i} \Rightarrow \sum_{i=1}^{n} f_{i} \cdot\left(x_{i}-\bar{x}ight)=0$