The measure of variability indicating how many standard detions, an observation is above or below the mean is
**Core Concept**
The Z score measures the number of standard deviations an observation is away from the mean in a normal distribution. It is a statistical tool used to express the position of an individual data point relative to the mean value. The Z score is useful for identifying outliers and for comparing the variability of different datasets.
**Why the Correct Answer is Right**
The Z score is calculated as the difference between the individual data point and the mean, divided by the standard deviation. This calculation provides a standardized measure of how many standard deviations away from the mean the observation is. The Z score formula is Z = (X - μ) / σ, where X is the individual data point, μ is the mean, and σ is the standard deviation. The Z score is an essential concept in statistics and is widely used in research and data analysis.
**Why Each Wrong Option is Incorrect**
**Option B:** The standard error (S.E) is a measure of the variability of the mean, not a measure of how many standard deviations an observation is away from the mean. It is calculated as the standard deviation of the sampling distribution of the mean.
**Option C:** The standard deviation (S.D) is a measure of the spread or dispersion of a dataset, but it does not indicate how many standard deviations an observation is away from the mean. It is a measure of the variability of the data, not a measure of position.
**Option D:** The co-efficient of variation (CV) is a measure of relative variability, expressed as a percentage. It is calculated as the ratio of the standard deviation to the mean, multiplied by 100. It does not indicate how many standard deviations an observation is away from the mean.
**Clinical Pearl / High-Yield Fact**
When working with Z scores, it's essential to remember that a Z score of 0 indicates that the observation is equal to the mean, while a positive Z score indicates that the observation is above the mean, and a negative Z score indicates that the observation is below the mean.
**✓ Correct Answer: A. Z score. The measure of variability indicating how many standard deviations an observation is above or below the mean is the Z score.**