Answer:
A positive z-score indicates that a particular value is greater than the mean, a negative z-score indicates that a particular value is less than the mean, and a z-score of zero indicates that a particular value is equal to the mean.
Step-by-step explanation:
Examples: Calculating a Z-Score
Suppose we have the following dataset that shows the height (in inches) of a certain group of plants:
5, 7, 7, 8, 9, 10, 13, 17, 17, 18, 19, 19, 20
The sample mean of this dataset is 13 and the sample standard deviation is 5.51.
1. Find the z-score for the value “8” in this dataset.
Here is how to calculate the z-score:
z = (X – μ) / σ = (8 – 13) / 5.51 = -0.91
This means that the value “8” is 0.91 standard deviations below the mean.
2. Find the z-score for the value “13” in this dataset.
Here is how to calculate the z-score:
z = (X – μ) / σ = (13 – 13) / 5.46 = 0
This means that the value “13” is exactly equal to the mean.
3. Find the z-score for the value “20” in this dataset.
Here is how to calculate the z-score:
z = (X – μ) / σ = (20 – 13) / 5.46 = 1.28
Answer:
A positive z-score indicates that a particular value is greater than the mean, a negative z-score indicates that a particular value is less than the mean, and a z-score of zero indicates that a particular value is equal to the mean.
