Question

What could you do to every number in a list such that the standard deviation changes and what could you do to every number in that list such that the standard deviation stays the same?

Answer 1

The actual numbers does not matter. For standard deviation, its about the distance of each term from the mean.

Example:- the set {10, 20, 30} and the set {150, 160, 170} has the same standard deviation. So if we add or subtract the same value from every term in the set, the standard deviation will not change.

1.

• If you multiply or divide every term in the set by the same number, the standard deviation will change by that same number.
• Example if we multiply {10, 20, 30} by 2, we will get {20, 40, 60}. These numbers, on average, are further away from mean. The standard deviation of {20, 40, 60} is exactly double as compared to standard deviation of {10, 20, 30}.

2.

While adding or subtracting a constant from the distribution, the mean will change by the same constant value. The standard deviation will remain unchanged. This is because, we are just shifting the distribution up or down the scale. And we are not changing the distance between values.