In Mathematics and Statistics:
* Normalized data: Data that has been transformed to have a specific range, usually between 0 and 1 or -1 and 1. This is done to make comparisons between different datasets easier, as they are now on the same scale.
* Normalized vector: A vector that has a length of 1. This is achieved by dividing each component of the vector by its magnitude.
* Normalized distribution: A distribution that has been transformed to have a mean of 0 and a standard deviation of 1. This allows for easier comparison of different distributions.
In Computer Science and Engineering:
* Normalized database: A database where data redundancy is minimized and data consistency is maintained. This is achieved by breaking down data into smaller, related tables and linking them with foreign keys.
* Normalized signal: A signal that has been adjusted to have a specific amplitude or power level. This is often done to prevent distortion or clipping.
In General Use:
* Normalized: Something that has been made standard or typical. For example, a "normalized response" in a survey would be an answer that reflects the average or most common response.
To understand the specific meaning of "normalized," it's crucial to consider the context in which it's used.
Here are some examples to illustrate the various meanings:
* "The data was normalized to have a mean of 0 and a standard deviation of 1." (Statistical normalization)
* "The database was normalized to reduce data redundancy." (Database normalization)
* "The audio signal was normalized to prevent clipping." (Signal normalization)
* "The students' scores were normalized to account for different difficulty levels in the exams." (General use of "normalized" to mean standardized)