AP EAMCET · Maths · Statistics
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
- A It indicates a higher degree of dispersion of the observations from the mean \(\bar{x}\)
- B It indicates that there is no dispersion
- C \(\sum_{\mathrm{i}=1}^{\mathrm{m}}\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2\) is the arithmetic mean of the data
- D It indicates that each observation \(x_i\) is very close to the mean \(\bar{x}\) and hence degree of dispersion is low.
Answer & Solution
Correct Answer
(D) It indicates that each observation \(x_i\) is very close to the mean \(\bar{x}\) and hence degree of dispersion is low.
Step-by-step Solution
Detailed explanation
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.
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