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Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations. z-score for 10 -01.25 Incorrect: Your answer is incorrect. z-score for 20 1.25 Correct: Your answer is correct. z-score for 12 -.75 Correct: Your answer is correct. z-score for 17 .5 Correct: Your answer is correct. z-score for 16 .25 Correct: Your answer is correct.

Respuesta :

The calculations below show that Z-score of 10 is –1.25; Z-score of 20 is 1.25; Z-score of 12 is –0.75; Z-score of 17 is 0.50; and Z-score of 16 is 0.25.

How do we calculate a Z-score?

The following notations and formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

SD = Standard deviation = Variance^0.5

Z-score = (x - Mean) / SD

Where;

n = number of values = 5

x = each value

Therefore, we have:

Mean = (10 + 20 + 12 + 17 + 16) / 5 = 15

Variance = ((10-15)^2 + (20-15)^2 + (12-15)^2 + (17-15)^2 + (16-15)^2) / (5-1) = 64 / 4 = 16

SD = Standard deviation = Variance^0.50 = 16^0.5 = 4

Z-score of 10 = (10 – 15) / 4 = –1.25

Z-score of 20 = (20 - 15) / 4 = 1.25

Z-score of 12 = (12 - 15) / 4 = –0.75

Z-score of 17 = (17 - 15) / 4 = 0.50

Z-score of 16 = (16 - 15) / 4 = 0.25

Learn more about Z-score here: https://brainly.com/question/13871342.

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