Standardized score

Definition

A standardized score, also known as a z-score, indicates how many standard deviations an element is from the mean of its distribution. It allows for comparison between different sets of data by converting them into a common scale.

5 Must Know Facts For Your Next Test

1. A standardized score is calculated using the formula (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
2. Standardized scores have a mean of 0 and a standard deviation of 1 in a normal distribution.
3. Positive z-scores indicate values above the mean, while negative z-scores indicate values below the mean.
4. Z-scores can be used to determine the percentile rank of a data point within a normally distributed dataset.
5. Standardized scores are essential for comparing scores from different distributions or scales.

Review Questions

• How do you calculate a standardized score?
• What does it mean if a data point has a z-score of -2?
• Why are standardized scores important in statistics?

Related terms

Mean: The average value in a set of numbers, calculated as the sum divided by the count.

Standard Deviation: A measure of how spread out numbers are in a dataset.

Percentile Rank: The percentage of scores in its frequency distribution that are equal to or lower than it.