Question

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 z-score for 20 z-score for 12 z-score for 17 z-score for 16

Answer 1

The z-scores for the given data values are -1.25, 1.25, -0.75, 0.5, and 0.25.

Step-by-step explanation:

The z-score for a data value is a measure of how many standard deviations it is from the mean. To compute the z-score, we use the formula:

z = (x - mean) / standard deviation

1. For the data value 10: z = (10 - 15) / 4 = -1.25
2. For the data value 20: z = (20 - 15) / 4 = 1.25
3. For the data value 12: z = (12 - 15) / 4 = -0.75
4. For the data value 17: z = (17 - 15) / 4 = 0.5
5. For the data value 16: z = (16 - 15) / 4 = 0.25

Therefore, the z-scores for the given data values are:

• z-score for 10: -1.25
• z-score for 20: 1.25
• z-score for 12: -0.75
• z-score for 17: 0.5
• z-score for 16: 0.25