### what unit of measurement ios used to describe how far a sert of values are from the mean

standard deviation is the measure used to determine how values are from the mean

### Explain how to standardize a value.

Standardizing a value occurs by determining the difference between the value and the mean, divide by the standard deviation.

### Breifly describe why standardized units are used to compare values that are measured using different scales, different units, or different populations.

because units are eliminated, different types of data can be comparing using standardized units

### How does adding or subtracting a constant amount to each value in a set of data affect the mean? why does this happen?

Adding or subtracting a constant to each value affects the mean by that amount because the center is moved that amount

### How does multiplying or dividing a constant amount by each value in a set of data ( also called rescaling) affect the mean? Why does this happen?

Multiplying or dividing all values will have the same affect on the mean since all values are changing equally.

### How does adding or subtracting a constant amount to each value in a set of data affect te standard deviaton? Why does this happen?

Since the distance from center does not change, only the location of center, so standard deviation is unchanged.

### How does multiplying or dividing a constant amount by each value in a set or fata(also called rescaling) affect the standard deviation? Why does this happen?

Since the distance is affected by multiplying/dividing all values, the standard deviation is also changed.

### How does standardizing a variable affect the shape, center, and spread of its distribution?

Standardizing a variable does not change the shape of a distribution, the center changes mean to 0, and the spread changes by the standard diviation becomes 1.