The question asks about the change in the standard deviation when each piece of data is increased or decreased by a constant value, $n$.

Let's analyze the effect of such transformations on standard deviation:

1. Standard Deviation and Addition/Subtraction:
   • When you add or subtract the same constant, $n$, to each data point in a dataset, the overall spread of the data (how far data points are from the mean) does not change. Standard deviation measures the spread of data relative to the mean, and since all data points are shifted uniformly by $n$, the distances between them remain the same. Therefore, the standard deviation stays the same.

This leads us to the correct answer, which is:

• D. The standard deviation remains the same if each piece of data is increased, or decreased, by $n$.

Would you like a more detailed explanation or have any further questions?

Here are five related questions to expand on this concept:

1. How does multiplying each data point by a constant affect the standard deviation?
2. What is the relationship between variance and standard deviation?
3. How does adding a constant to the dataset affect the mean?
4. Can the standard deviation ever be negative?
5. How does the standard deviation change when data points are more dispersed?

Tip: Remember that standard deviation is only influenced by how spread out the data is, not the specific values themselves.