Respuesta :
Answer:
True
Step-by-step explanation:
Standard scores, also known as z-scores, are raw scores that have been adjusted for the particular mean and standard deviation of the distribution from which they are derived. They express the score's relation to the mean in terms of standard deviations.
Final answer:
The statement is true; standard scores are raw scores that have been adjusted using the mean and standard deviation of the distribution they come from, with z-scores being a common example. This standardization allows for fair comparisons across different scales or distributions.
Explanation:
The statement is true; standard scores are indeed raw scores that have been transformed using the mean and standard deviation of the distribution from which the raw scores were obtained. This transformation process is known as standardization. A common standard score is the z-score, which is calculated by subtracting the mean of the distribution from the raw score and then dividing the result by the standard deviation of the distribution. This process yields a score that reflects how many standard deviations away from the mean the raw score is.
The formula for calculating a z-score is given by:
Z = (X - μ) / σ, where Z represents the z-score, X is the raw score, μ (mu) is the mean of the distribution, and σ (sigma) is the standard deviation.
Standard scores are very useful in comparing test results or any data that come from different populations or distributions. For example, if in one class, students are graded out of 100 and in another class out of 50, comparing the raw scores directly doesn't make sense because the scales are different. However, by converting these to z-scores, students' performances can be compared fairly because the scores are now on the same standardized scale with a mean of 0 and a standard deviation of 1, regardless of the original scale.
Standardization is often used in educational testing, psychology, and many other fields to compare scores that are on different scales or have different distributions. It is also useful when the data needs to be normalized, like when employing statistical techniques that assume a normal distribution.
