Which of the following is true from the equation: $\sum_{i}\left(x_{1}-\bar{x}\right)$
= 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

Which of the following is true from the equation: $\sum_{i}\left(x_{1}-\bar{x}\right)$
 = 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

Quizplus · Accepted Answer

The equation $\sum_{i}\left(x_{1}-\bar{x}\right)=0$ means that the sum of the deviations of each data point from the mean is equal to zero. This implies that for every data point above the mean, there must be a corresponding data point below the mean that has an equal deviation from the mean. Therefore, the sum of deviations above the mean is the same as the sum of deviations below the mean, and choice A is the correct answer. Choice B and D cannot be true because the equation only considers the deviations from the mean and not the actual values of the data points. Choice C cannot be inferred from the given equation.

Which of the Following Is True from the Equation ∑i(x1−xˉ)\sum_{i}\left(x_{1}-\bar{x}\right)∑i​(x1​−xˉ) = 0 Where

Which of the Following Is True from the Equation $\sum_{i}\left(x_{1}-\bar{x}\right)$ = 0 Where