If $x_1, x_2, \ldots x_n$ are ' $n$ ' observations and $x$ is their mean. If…
If $x_1, x_2, \ldots x_n$ are ' $n$ ' observations and $x$ is their mean. If $\sum_{i=1}^n\left(x_1-\bar{x}\right)^2$ is almost zero, then a true statement among the following is
It indicates a higher degree of dispersion of the observations from the mean $\bar{x}$
It indicates that there is no dispersion
$\sum_{\mathrm{i}=1}^{\mathrm{m}}\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2$ is the arithmetic mean of the data
It indicates that each observation $x_i$ is very close to the mean $\bar{x}$ and hence degree of dispersion is low.
Solution
Since $\sum_{\mathrm{i}=1}^{\mathrm{n}}\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2$ is almost zero. So it indicates
that each observation $x_{\hat{i}}$ is very close to the $\bar{x}$. Hence degree of dispersion is low.