Ch. 5 Notes

What do sampling distributions show?

How much the means of samples vary

When we shift the data by adding (or subtracting) a constant to each value, all measures of position (center, percentiles, min, max) will ....

Increaze (or decrease) by the same constant

Data values below the mean have a ___ z-score

Negative

True/false: adding (or subtracting) a constant to every data value adds (or subtracts) the same constant to measures of position, but leaves measures of spread unchanged

True

True/false: multiplying or dividing each value by a constant - rescaling the data - changed the measurement units

True

True/false: standardizing may change the center and spread values, but it does NOT affect the shape of the distribution. A histogram or box plot of standardized values looks just the same as the histogram or box plot of the original values, except for the numbers

True

True/false: when we subtract the mean of the data from every data value, we shift the mean to zero. This shift does not change the standard deviation

True

The standard normal model is ___ and ___ and there are no obvious ____

Unimodal, symmetric, outliers

How does standardizing affect the distribution of a variable?

- standardizing into z-scores does NOT change the shape of the distribution of a variable - standardizing into z-scores changes the center by making the mean 0 - standardizing into z-scores changes the spread by making the standard deviation 1

What does adding or subtracting a constant value do to the spread of the distribution?

Adding or subtracting a constant changes each data value equally, so the entire distribution just shifts. It's shape does not change and neither does the spread (range, IQR, Standard Deviation)

What happens to the mean of the distribution when you add or divide each value by a constant?

Box plot and 5-number summaries show that all measures of position act the same way. They all get multiplied by the constant

What happens to the spread of the distribution when you add or divide each value by a constant?

Box plot and 5-number summaries show that all measures of position act the same way. They all get multiplied by the constant

What happens to the shape of the distribution when you add or divide each value by a constant?

Shape really hasn't changed