When data values are standardized, what statistical measures are used to transform them?

When data values are standardized, what statistical measures are used to transform them?

• A. Median and variance
• B. Mean and standard deviation
• C. Mode and interquartile range
• D. Sum and average

Answer: (B)

When data values are standardized, they are transformed using the mean and standard deviation of the dataset. Standardization is the process of rescaling the data so that it has a mean of zero and a standard deviation of one. This is achieved by subtracting the mean from each data point and then dividing by the standard deviation. The formula for standardization is given by: \[ Z = \frac{(X - \mu)}{\sigma} \] where \( Z \) is the standardized score, \( X \) is the original data value, \( \mu \) represents the mean of the dataset, and \( \sigma \) represents the standard deviation. By transforming data in this way, we can compare datasets with different units or scales more effectively, as the standardized values reflect how many standard deviations a data point is from the mean. In contrast, the other options mention statistical measures that are not used in the standardization process. The median is a measure of central tendency that is relevant in other contexts, but it does not factor into the transformation for standardization. The mode is also a measure of central tendency, while the interquartile range is a measure of statistical dispersion, neither of which relates to calculating standardized scores. Additionally, the

When data values are standardized, they are transformed using the mean and standard deviation of the dataset. Standardization is the process of rescaling the data so that it has a mean of zero and a standard deviation of one. This is achieved by subtracting the mean from each data point and then dividing by the standard deviation.

The formula for standardization is given by:

[ Z = \frac{(X - \mu)}{\sigma} ]

where ( Z ) is the standardized score, ( X ) is the original data value, ( \mu ) represents the mean of the dataset, and ( \sigma ) represents the standard deviation. By transforming data in this way, we can compare datasets with different units or scales more effectively, as the standardized values reflect how many standard deviations a data point is from the mean.

In contrast, the other options mention statistical measures that are not used in the standardization process. The median is a measure of central tendency that is relevant in other contexts, but it does not factor into the transformation for standardization. The mode is also a measure of central tendency, while the interquartile range is a measure of statistical dispersion, neither of which relates to calculating standardized scores. Additionally, the