# Statistics Chapter 3

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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

Example: