Final answer:
False. The standard deviation does not remain unchanged when the mean of a data set changes.
Step-by-step explanation:
False. The standard deviation does not remain unchanged when the mean of a data set changes. The standard deviation measures the spread or variability of the data around the mean. When the mean of a data set changes, the distance between each data point and the new mean will change, resulting in a different spread or variability. For example, if the mean shifts to a higher value, the data points will generally be further away from the new mean, resulting in a larger standard deviation.