One reason for standardizing random variables is to measure variables with:
A. dissimilar means and similar standard deviations in like terms
B. different means and standard deviations on a non-standard scale
C. similar means and standard deviations on two scales
D. different means and standard deviations on a single scale
The correct answer is A. dissimilar means and similar standard deviations in like terms.
To understand why standardizing random variables is used in this context, let's first define what it means to standardize a random variable. Standardizing a random variable involves subtracting the mean of the variable from each observation and then dividing it by the standard deviation of the variable. This process creates a new random variable with a mean of 0 and a standard deviation of 1.
In statistical analysis, it is often necessary to compare or combine variables that have different means and standard deviations. Standardizing the random variables allows us to put them on a common scale, making it easier to compare them. By doing so, we can analyze the variables in like terms, eliminating the influence of their original means and standard deviations.
Option A states that standardizing random variables is done to measure variables with dissimilar means and similar standard deviations in like terms. This means that although the variables may have different means, they have similar variability (standard deviation). By standardizing them, we can compare and analyze these variables in a meaningful way, ensuring that they are measured in like terms.
In contrast, the other options B, C, and D do not accurately describe the purpose of standardizing random variables. Option B mentions different means and standard deviations on a non-standard scale, which is not the common goal of standardization. Option C suggests similar means and standard deviations on two scales, which is not the standardization process. Option D refers to different means and standard deviations on a single scale, which is not typically the case after standardizing random variables.