Question

consider a sample with the following data values. 62 90 50 86 72 compute the z-scores for the above five observations. (round your answers to two decimal places.)

Answer 1

To compute the z-scores for the given data values, find the mean and standard deviation. Then, use the formula z = (x - μ) / σ to calculate the z-scores for each data value.

Step-by-step explanation:

To compute the z-scores for the given data values, we need to first find the mean and standard deviation.

Mean (μ) = (62 + 90 + 50 + 86 + 72) / 5 = 72

Standard Deviation (σ) = sqrt(((62 - 72)^2 + (90 - 72)^2 + (50 - 72)^2 + (86 - 72)^2 + (72 - 72)^2) / 5) ≈ 15.13

Now, we can calculate the z-scores using the formula: z = (x - μ) / σ

For the data values: 62, 90, 50, 86, and 72:

z-score of 62 = (62 - 72) / 15.13 ≈ -0.66

z-score of 90 = (90 - 72) / 15.13 ≈ 1.19

z-score of 50 = (50 - 72) / 15.13 ≈ -1.45

z-score of 86 = (86 - 72) / 15.13 ≈ 0.93

z-score of 72 = (72 - 72) / 15.13 = 0