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Measure of Center

A value at the center or middle of a data set

Mean

The measure of center found by adding the data values and dividing by the total number of data values

Sample Size

The number of sample values, denoted by "n"

"x bar"

The mean of a set of sample values

Does not vary as much as other measures of center

What is an advantage of using the mean versus other measures of center?

It is more resistant to outliers

What is an advantage to using the median versus other measures of center?

Median

the measure of center that is the middle value when the original data values are arranged in order of increasing or decreasing magnitude. "~ over x = x tilde"

Mode

The value that occurs with the greatest frequency

Bimodal

when two data values occur with the same greatest frequency, each one is a mode and the data set is:

Multimodal

When more than two data values occur with the same greatest frequency, each is a mode and the data set is said to be:

No mode

When no data value is repeated, the data set is said to have:

mode

What measure of center is the only one that can be used at the nominal level?

Midrange

What measure of center is so sensitive to outliers that it is rarely used?

Midrange

A measure of center that is the value midway between the maximum and minimum values in the original data set.

( maximum data value + minimum data value) / 2

Formula for midrange

Round-off Rule

Carry one more decimal place than is present in the original set of values

sum of ( frequency * x) / sum of all frequencies

formula for mean from frequency distribution (use class midpoints)

weighted mean

data values are assigned different weights

sum of (w * x) / sum of w

formula for weighted mean

skewed

A distribution of data is ___________ if it is not symmetric and extends more to one side than to the other.

Skewed to the left (also called negatively skewed)

Data that has a longer left tail, and the mean and median are to the left of the mode.

Skewed to the right (also called positively skewed)

Data that has a longer right tail, and the mean and median are to the right of the mode

No

Can the mean and the median always be used to identify the shape of the distribution? (Yes/No)

Range

The difference between the maximum data value and the minimum data value

max data value - min data value

formula for range

too sensitive to outliers

What is the downfall of range?

round-off rule for measures of variation

When rounding the value of a measure of variation, carry one more decimal place than is present in the original set of data

Standard Deviation (denoted by s)

The ____ ____ of a set of sample values is a measure of variation of values about the mean.

positive

Is standard deviation usually negative or positive?

zero

When all the data values are the same number, the standard deviation is

greater amounts of variation

Larger values for standard deviation indicate

original data values

The units on standard deviation are the same as the

Variance

The _______ of a set of values is a measure of variation equal to the square of the standard deviation.

Different

The units of variance are (same/different) than the units of the original data

Range rule of thumb

For many data sets, the vast majority of sample values lie within two standard deviations of the mean. This is called the:

mean - 2 * standard deviation

minimum "usual" value formula

mean + 2 * standard deviation

maximum "usual" value formula

unusual

A value is ______ if it differs from the mean by more than two standard deviations

Empirical Rule

for data sets that are bell shaped, 68% will be within one standard deviation, 95% will be within two deviations, and 99.7% will be within three deviations. This is called the:

mean absolute deviation

sum of ( absolute value of ( x - "x bar")) / n

Coefficient of Variation

The ________ ___ _______ for a set of nonnegative sample or population data, expressed as a percent, describes the standard deviation relative to the mean