Statistics Chapter 3
Measure of Center
A value at the center or middle of a data set
The measure of center found by adding the data values and dividing by the total number of data values
The number of sample values, denoted by "n"
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?
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"
The value that occurs with the greatest frequency
when two data values occur with the same greatest frequency, each one is a mode and the data set is:
When more than two data values occur with the same greatest frequency, each is a mode and the data set is said to be:
When no data value is repeated, the data set is said to have:
What measure of center is the only one that can be used at the nominal level?
What measure of center is so sensitive to outliers that it is rarely used?
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
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)
data values are assigned different weights
sum of (w * x) / sum of w
formula for weighted mean
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
Can the mean and the median always be used to identify the shape of the distribution? (Yes/No)
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.
Is standard deviation usually negative or positive?
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
The _______ of a set of values is a measure of variation equal to the square of the standard deviation.
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
A value is ______ if it differs from the mean by more than two standard deviations
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