statistics Ch 1-4

Changing the mean & standard deviation of a distribution.

If a constant is added to each score in a distribution the mean for the distribution changes, but the variance & standard deviation does not.

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.

what unit of measurement is used to describe how far a set of values are from the mean

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

When you add or subtract a constant from each score in a distribution

the mean changes by the amount added or subtracted; but the standard deviation & variance remain the same.

What is meant by a distribution?

A distribution gives possible values of the variable and the frequency or ralative frequency of each value

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 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.

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.

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.

Range

Tell you the largest difference that you have among your scores. It is strongly affected by outliers, & being based on only two scores it can be very unreliable.

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

Adding a score changes the sum of all the scores

but Not the spread or shape of a distribution.

Standard Deviation

is a good descriptive measure of variability, although it can be affected strongly by outliers.

Multiplying or dividing by a constant

means you will multiply or divide the original mean, the standard deviation & variance by the same constant too.