Question

Given the following set of scores \[ X: 10,12,6,8,9,11,13,13,5,0,1 \] What is the value of \( \sum(X-\bar{X}) \) a. \( 4.54 \) b. 0 c. 206 d. 1

Answer 1

The sum of the deviations of each score from the mean
`(\( \bar{X} \))` in the given set is 206, indicating the overall dispersion of scores from the mean.

c. 206

Step-by-step explanation:

The given expression
`\( \sum(X-\bar{X}) \) represents the sum of the deviations of individual scores from the mean (\( \bar{X} \)). First, calculate the mean (\( \bar{X} \))`of the given set of scores, which is the sum of all scores divided by the number of scores:

`\[ \bar{X} = (10+12+6+8+9+11+13+13+5+0+1)/(11) = (88)/(11) = 8 \]`

Now, substitute the mean into the expression
`\( \sum(X-\bar{X}) \)`and simplify:

`\[ \sum(X-\bar{X}) = (10-8) + (12-8) + (6-8) + (8-8) + (9-8) + (11-8) + (13-8) + (13-8) + (5-8) + (0-8) + (1-8) \]\[ = 2 + 4 -2 + 0 + 1 + 3 + 5 + 5 -3 -8 -7 = 206 \]`

Therefore, the correct answer is option c, 206, as it represents the sum of the deviations of individual scores from the mean in the given set. This value gives an indication of the overall dispersion of the scores from the mean.