Z Scores Flashcards
What is a Z-score?
A Z-score measures how far a value is from the mean in terms of standard deviations.
What is the formula for calculating a Z-score?
Z=X−μ/σ
Where:
𝑋 = individual score
𝜇 = population mean
𝜎 = population standard deviation
What does a Z-score of 0 indicate?
That the value is exactly equal to the mean.
What does a positive Z-score mean?
The value is above the mean.
What does a negative Z-score mean?
The value is below the mean.
What are the properties of Z-scores?
Mean of Z-scores = 0
Standard deviation of Z-scores = 1
Retains the shape of the original distribution
Why are Z-scores useful?
Standardizing scores across different distributions.
Comparing values from different datasets.
Identifying outliers.
Calculating probabilities in a normal distribution.
How do Z-scores help in comparing different distributions?
By converting different scales into a standard unit of measure, allowing meaningful comparisons.
How are Z-scores used to detect outliers?
Scores with ∣Z∣>3 are considered potential outliers.
What is the relationship between Z-scores and the normal distribution?
Z-scores correspond to areas under the normal curve, allowing probability estimation.
What percentage of data falls within ±1 standard deviation in a normal distribution?
About 68%.
What percentage of data falls within ±2 standard deviations in a normal distribution?
About 95%.
What is the standard normal distribution?
A normal distribution with a mean of 0 and a standard deviation of 1.
What are the properties of a standard normal distribution?
Bell-shaped and symmetrical.
Mean = 0, Standard Deviation = 1.
Defined by the empirical rule.
How do Z-scores relate to probability?
Z-scores can be used with normal distribution tables to determine the probability of a score occurring within a distribution.
