Explanation:

Standard deviation is a measure of dispersion or variability of a set of data from its mean. It tells us how spread out the data is from the average.

Independence of Change of Origin:

The mean and standard deviation are affected by a change of origin. For instance, if we add a constant to each data point, the mean will also shift by that constant. However, the standard deviation will remain the same. For example, if we have the data set {1, 2, 3} with a mean of 2 and a standard deviation of 0.82, adding 5 to each data point will result in {6, 7, 8} with a mean of 7 and a standard deviation of 0.82.

Independence of Change of Scale:

Similarly, the mean and standard deviation are affected by a change of scale. For example, if we multiply each data point by a constant, the mean will also be multiplied by that constant. However, the standard deviation will be multiplied by the absolute value of that constant. For instance, if we have the data set {1, 2, 3} with a mean of 2 and a standard deviation of 0.82, multiplying each data point by 3 will result in {3, 6, 9} with a mean of 6 and a standard deviation of 2.46.

Independence of Both Origin and Scale:

The standard deviation is independent of a change of origin but not of a change of scale. Therefore, the correct answer is option B, which is "independent of change of origin."