Question

a. the mean is 58. (simplify your answer.) b. complete the following table by entering the deviations for each data value. (simplify your answers.) 28 - 30 78 20 53 - 5 28 - 30 103 45 c. the sum of the deviations is (simplify your answer.)

Explanation:

Step1: Identify the deviations

The deviations from the mean (which is 58) are given as: -30, 20, -5, -30, 45. Wait, no, actually, the data values are 28, 78, 53, 28, 103, and their deviations from the mean (58) are calculated as data value - mean. But in the table, the deviations are already provided: -30 (for 28: 28 - 58 = -30), 20 (for 78: 78 - 58 = 20), -5 (for 53: 53 - 58 = -5), -30 (for 28: 28 - 58 = -30), 45 (for 103: 103 - 58 = 45). So we need to sum these deviations: -30 + 20 + (-5) + (-30) + 45.

Step2: Sum the deviations

First, add -30 and 20: $-30 + 20 = -10$.
Then add -5 to that result: $-10 + (-5) = -15$.
Then add -30 to that: $-15 + (-30) = -45$.
Then add 45 to that: $-45 + 45 = 0$.

Answer:

0