Which of the following is true from the equation: $\sum \left( x _ { i } - \bar { x } \right)$ = 0, where $ \bar{x} $ is the mean of the sample?
A) The sum of the deviations above the mean are the same as the sum of the deviations below the mean
B) Half the data lie above the mean of the values
C) The specific set of values does not have any outliers affecting the mean
D) Half the data lie below the mean of the values

Question

Quizplus · Accepted Answer

The equation $\sum \left( x _ { i } - \bar { x } \right) = 0$ indicates that the sum of the deviations from the mean (both above and below the mean) equals zero. This means that the positive deviations (above the mean) exactly offset the negative deviations (below the mean), supporting choice A. It does not imply anything about the proportion of data above or below the mean, the presence of outliers, or the distribution of the data.

Which of the Following Is True from the Equation ∑(xi−xˉ)\sum \left( x _ { i } - \bar { x } \right)∑(xi​−xˉ)

Which of the Following Is True from the Equation $\sum \left( x _ { i } - \bar { x } \right)$