Z-Score
The Z-score, also known as the standard score, is a statistical measure that quantifies how many standard deviations a particular data point is away from the mean of a distribution
The Z-score, also known as the standard score, is a statistical measure that quantifies how many standard deviations a particular data point is away from the mean of a distribution. It is used to compare and interpret individual data points within a dataset and determine their relative position.
To compute the Z-score, you subtract the mean from the data point and divide the result by the standard deviation of the dataset. The formula for a Z-score is:
Z = (X – μ) / σ
Where:
Z is the Z-score
X is the individual data point
μ is the mean of the dataset
σ is the standard deviation of the dataset
The resulting Z-score can be positive or negative, indicating whether the data point is above or below the mean, respectively. A Z-score of 0 means that the data point is exactly at the mean.
Z-scores are useful because they allow for the comparison of data points from different datasets, even if they have different units or scales. Additionally, they provide insights into the relative rarity or normality of a particular data value within a distribution. A Z-score can be used to determine how likely or unusual a data point is in comparison to the rest of the dataset.
For example, if you have a dataset of exam scores with a mean of 75 and a standard deviation of 10, and a student scores 85 on the exam, you can compute their Z-score as:
Z = (85 – 75) / 10 = 1
This means the student’s score is 1 standard deviation above the mean, indicating that their performance is better than approximately 84% of the other students in the class.
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