2. For a distribution of scores, which of the following Z score values represents the location closest to the mean?
What are your choices?
Z score of zero is on the mean. Does that help?
To determine which Z-score value represents the location closest to the mean in a distribution of scores, you need to consider the characteristics of the Z-score.
A Z-score measures the number of standard deviations a particular score is from the mean. The mean has a Z-score of 0, indicating it is the reference point for calculating the Z-scores of other values in the distribution.
Given that the Z-scores are measured in standard deviations, the Z-score closest to the mean will have the smallest absolute value. In other words, it will be the Z-score that is closest to 0.
For example, if the choices for Z-score values are -1.5, 0.5, -0.2, and 0.7, you would compare their absolute values:
- |-1.5| = 1.5
- |0.5| = 0.5
- |-0.2| = 0.2
- |0.7| = 0.7
From the absolute values, you can see that -0.2 has the smallest absolute value. Therefore, the Z-score value closest to the mean is -0.2.
To find the closest Z-score value in a given set of choices, calculate the absolute value of each Z-score and select the value with the smallest absolute value.
To determine which Z score value represents the location closest to the mean in a distribution of scores, you need to know the values of the Z scores and their corresponding locations. The Z score measures the number of standard deviations a score is from the mean.
In a normal distribution, a Z score of 0 represents the location exactly at the mean. Any positive Z score represents a location to the right of the mean, and any negative Z score represents a location to the left of the mean.
Therefore, the Z score closest to the mean is 0, as it represents the location exactly at the mean.