When a certain value is added to each number in a set, what happens to the standard deviation?

When a certain value is added to each number in a set, what happens to the standard deviation?

• A. The standard deviation increases
• B. The standard deviation decreases
• C. The standard deviation does not change
• D. The standard deviation becomes negative

Answer: (C)

When a constant value is added to each number in a set, the standard deviation remains unchanged. This is because standard deviation is a measure of the dispersion or spread of a set of values around the mean. Adding a constant shifts the entire dataset up or down but does not affect how spread out the values are from one another. For example, if all values in a set are increased by a certain number, the differences between any two values remain the same; therefore, the variability among the set doesn’t change. The calculations for the standard deviation involve these deviations from the mean, and since those deviations do not change when a constant is added, the standard deviation itself is unaffected. Thus, the correct answer indicates that the standard deviation does not change when a specific value is added to every element of a set.

When a constant value is added to each number in a set, the standard deviation remains unchanged. This is because standard deviation is a measure of the dispersion or spread of a set of values around the mean.

Adding a constant shifts the entire dataset up or down but does not affect how spread out the values are from one another. For example, if all values in a set are increased by a certain number, the differences between any two values remain the same; therefore, the variability among the set doesn’t change. The calculations for the standard deviation involve these deviations from the mean, and since those deviations do not change when a constant is added, the standard deviation itself is unaffected.

Thus, the correct answer indicates that the standard deviation does not change when a specific value is added to every element of a set.