Question

The mean of a data set is equal to $10$ and its standard deviation is equal to $1$. If we add $5$ to each data value, then what will happen to the mean and standard deviation of the new data.

Answer 1

Since $5$ is added to all data values, the mean will also increase by $5$ and becomes $15$. But the standard deviation which measure the "distance" between the mean and the data values does not change.