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Questions and Answers
What does a Z score of 0 indicate?
What does a Z score of 0 indicate?
- The observed value is three standard deviations above the mean
- The observed value is two standard deviations below the mean
- The observed value is equal to the mean (correct)
- The observed value is one standard deviation above the mean
What is the formula for calculating a Z score?
What is the formula for calculating a Z score?
- Z = (X × μ) / σ
- Z = (X + μ) / σ
- Z = (X - μ) / σ (correct)
- Z = (X ÷ μ) / σ
What does a Z score greater than 2 indicate?
What does a Z score greater than 2 indicate?
- The observed value is three standard deviations below the mean
- The observed value is one standard deviation above the mean
- The observed value is two standard deviations above the mean (correct)
- The observed value is two standard deviations below the mean
What is one of the uses of Z scores?
What is one of the uses of Z scores?
What does a Z score less than -1 indicate?
What does a Z score less than -1 indicate?
What is the purpose of standardizing values using Z scores?
What is the purpose of standardizing values using Z scores?
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Study Notes
Z Score
Definition
A Z score, also known as a standard score, is a statistical measurement that indicates how many standard deviations an observation is away from the mean of a normal distribution.
Formula
The Z score formula is:
Z = (X - μ) / σ
Where:
- Z = Z score
- X = observed value
- μ = mean of the distribution
- σ = standard deviation of the distribution
Interpretation
A Z score of:
- 0 indicates that the observed value is equal to the mean
- Greater than 0 indicates that the observed value is above the mean
- Less than 0 indicates that the observed value is below the mean
- Greater than 1 or less than -1 indicates that the observed value is one standard deviation away from the mean
- Greater than 2 or less than -2 indicates that the observed value is two standard deviations away from the mean
- Greater than 3 or less than -3 indicates that the observed value is three standard deviations away from the mean
Uses
Z scores are used in various statistical applications, including:
- Identifying outliers in a dataset
- Comparing values from different normal distributions
- Calculating percentiles and percent ranks
- Standardizing values for comparison purposes
Z Score
- A Z score is a statistical measurement that indicates how many standard deviations an observation is away from the mean of a normal distribution.
Formula
- Z score formula: Z = (X - μ) / σ
- Where Z = Z score, X = observed value, μ = mean of the distribution, and σ = standard deviation of the distribution
Interpretation
- Z score of 0: observed value is equal to the mean
- Z score greater than 0: observed value is above the mean
- Z score less than 0: observed value is below the mean
- Z score greater than 1 or less than -1: observed value is one standard deviation away from the mean
- Z score greater than 2 or less than -2: observed value is two standard deviations away from the mean
- Z score greater than 3 or less than -3: observed value is three standard deviations away from the mean
Uses
- Identify outliers in a dataset
- Compare values from different normal distributions
- Calculate percentiles and percent ranks
- Standardize values for comparison purposes
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