Final answer:
The sum of squares of the deviations from the mean for the given ACT scores (13, 24, 27, 30, and 22) is 166.8.
Step-by-step explanation:
To find the sum of squares of the deviations from the mean of ACT scores 13, 24, 27, 30, and 22, we first calculate the mean of these scores. Add them together and divide by the number of scores: (13 + 24 + 27 + 30 + 22) / 5 = 116 / 5 = 23.2. This is the mean score.
Next, find the deviations from the mean for each score, square these deviations, and sum them up. The deviations are (13 - 23.2), (24 - 23.2), (27 - 23.2), (30 - 23.2), and (22 - 23.2). Squaring each and then summing gives:
- (13 - 23.2)^2 = 104.04
- (24 - 23.2)^2 = 0.64
- (27 - 23.2)^2 = 14.44
- (30 - 23.2)^2 = 46.24
- (22 - 23.2)^2 = 1.44
The sum of squares of these deviations is 104.04 + 0.64 + 14.44 + 46.24 + 1.44 = 166.8.