Data Set 5-7: 2, -2, 4, 6
-A raw score of -2 in Data Set 5-7 has a z score of
A) 1.52
B) -1.32
C) -1.52
D) 1.69.

Question

Quizplus · Accepted Answer

To find the z-score, use the formula z = (X - μ) / σ. The mean (μ) of the data set is (2 + (-2) + 4 + 6) / 4 = 2.5. The standard deviation (σ) is calculated as √[(1/4)((2-2.5)² + (-2-2.5)² + (4-2.5)² + (6-2.5)²)] = √[(1/4)(0.25 + 20.25 + 2.25 + 12.25)] = √[(1/4)(35)] = √8.75 ≈ 2.96. The z-score for -2 is (-2 - 2.5) / 2.96 ≈ -1.52.