What is the effect of multiplying all values in a dataset by a constant factor k?

What is the effect of multiplying all values in a dataset by a constant factor k?

• A. The median remains the same
• B. Mean is multiplied by k, standard deviation is multiplied by k
• C. The minimum and maximum values are unaffected
• D. Standard deviation is doubled

Answer: (B)

When you multiply all values in a dataset by a constant factor \( k \), the impact on statistical measures can be analyzed through their definitions. The mean, which represents the average of the dataset, is directly affected by multiplication. Specifically, when all individual values are multiplied by \( k \), the overall sum of the values increases by the same factor \( k \). Consequently, since the mean is the total sum divided by the number of values, it also gets multiplied by \( k \). Similarly, the standard deviation, which measures the dispersion or spread of the dataset, also responds to this multiplication. The standard deviation reflects how much individual data points deviate from the mean. By scaling all values by \( k \), the distances from the mean increase, and thus the standard deviation itself is multiplied by \( k \). This understanding establishes that the mean is indeed multiplied by \( k \) and the standard deviation is also multiplied by \( k \). In contrast, the median would adjust depending on \( k \): if \( k \) is positive, the median shifts in proportion to the values; if \( k \) is negative, it could also reverse the order, changing the median's position in the dataset. The minimum and maximum

When you multiply all values in a dataset by a constant factor ( k ), the impact on statistical measures can be analyzed through their definitions.

The mean, which represents the average of the dataset, is directly affected by multiplication. Specifically, when all individual values are multiplied by ( k ), the overall sum of the values increases by the same factor ( k ). Consequently, since the mean is the total sum divided by the number of values, it also gets multiplied by ( k ).

Similarly, the standard deviation, which measures the dispersion or spread of the dataset, also responds to this multiplication. The standard deviation reflects how much individual data points deviate from the mean. By scaling all values by ( k ), the distances from the mean increase, and thus the standard deviation itself is multiplied by ( k ).

This understanding establishes that the mean is indeed multiplied by ( k ) and the standard deviation is also multiplied by ( k ).

In contrast, the median would adjust depending on ( k ): if ( k ) is positive, the median shifts in proportion to the values; if ( k ) is negative, it could also reverse the order, changing the median's position in the dataset. The minimum and maximum