When the deviation scores, ( $X$ - $\overline { \mathrm { X } }$ ), are examined, your text noted two mathematical characteristics of the mean. These two characteristics involved
A) the maximum size of the mean and the minimum size of the mean
B) the size of the deviations when the mean is positive and the size when the mean is negative
C) the sum of the deviations and the size of the sum of the squared deviations
D) the maximum size of the deviations and their minimum size.

Question

Quizplus · Accepted Answer

The two mathematical characteristics of the mean when examining deviation scores ($X - \overline{X}$) are: 1) the sum of the deviations around the mean is always zero, and 2) the sum of the squared deviations is minimized when calculated from the mean, compared to any other value. This is why choice C is correct, as it refers to the sum of the deviations (which is zero) and the size (or sum) of the squared deviations, which is a key concept in variance and standard deviation calculations.

When the Deviation Scores, XXX - X‾\overline { \mathrm { X } }X

When the Deviation Scores, $X$ - $\overline { \mathrm { X } }$