Chapter 3: Descriptive Statistics: Numerical Measures Flashcards
sample statistics
a numerical value used as a summary measure for a sample (ex. the sample mean, x bar, the sample variance, s^2, and the sample standard deviation, s)
population parameter
a numerical value used as a summary measure for a population (ex. the population mean, u, the population variance, o^2, and the population standard deviation, o)
point estimator
a sample statistic, such as x bar, s^2, and s, used to estimate the corresponding population parameter.
mean
a measure of central location computed by summing the data values and dividing by the number of observations.
median
a measure of central location provided by the value in the middle when the data are arranged in ascending order.
mode
a measure of central location, defined as the value that occurs with greatest frequency.
weighted mean
the mean obtained by assigning each observation a weight that reflects its importance.
geometric mean
a measure of location that is calculated by finding the nth root of the product of n values.
percentile
a value that provides information about how the data are spread over the interval from the smallest to the largest value
pth percentile
for a data set containing n observations, the pth percentile divides the data into two parts: approximately p% of the observation are less that the pth percentile and approximately (100-p)% of the observations are greater than the pth percentile.
quartiles
the 25th, 50th, and 75th percentiles, referred to as the first, second (median), and third quartile, respectively. the quartiles can be used to divide a data set into four parts, with each part containing approximately 25% of the data.
range
a measure of variability, defined to be the largest value minus the smallest value.
interquartile range (IQR)
a measure of variability, defined to be the difference between the third and first quartiles
variance
a measure of variability based on the squared deviations of the data values about the mean.
standard deviation
a measure of variability computed by taking the positive square root of the variance.
coefficient of variation
a measure of relative variability computed by dividing the standard deviation by the mean and mulptiplying by 100
skewness
a measure of the shape of a data distribution. data skewed to the left=negative skewness. skewed to the right=positive skewness. symmetrical data=zero skewness
z-score
a value computed by dividing the deviation about the mean (xi-x bar) by the standard deviation s. a z-score is referred to as a standardized value and denotes the number of standard deviations xi is from the mean.
chebyshev’s theorem
a theorem that can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean
emperical rule
a rule that can be used to compute the percentage of data values that must be within one, two and three standard deviations of the mean for the data that exhibit a bell-shaped distribution.
outlier
an unusually small or large data value
five number summary
a technique that uses 5 numbers to summarize the data: smallest value, 1st quartile, median, 3rd quartile, largest value
box plot
a graphical summary of data based on a 5 number summary
covariance
a measure of linear association between two variables. positive values=positive relationship. negative values=negative relationship.
correlation coefficient
a measure of linear association between two variables that takes on values between -1 and +1. values near +1 indicate a strong positive linear relationship. values near -1 indicate a strong negative linear relationship. and values near zero lack any liner relationship.
a numerical value used as a summary measure for a sample (ex. the sample mean, x bar, the sample variance, s^2, and the sample standard deviation, s)
sample statistics
a numerical value used as a summary measure for a population (ex. the population mean, u, the population variance, o^2, and the population standard deviation, o)
population parameter
a sample statistic, such as x bar, s^2, and s, used to estimate the corresponding population parameter.
point estimator
a measure of central location computed by summing the data values and dividing by the number of observations.
mean
a measure of central location provided by the value in the middle when the data are arranged in ascending order.
median
a measure of central location, defined as the value that occurs with greatest frequency.
mode
the mean obtained by assigning each observation a weight that reflects its importance.
weighted mean
a measure of location that is calculated by finding the nth root of the product of n values.
geometric mean
a value that provides information about how the data are spread over the interval from the smallest to the largest value
percentile
for a data set containing n observations, the pth percentile divides the data into two parts: approximately p% of the observation are less that the pth percentile and approximately (100-p)% of the observations are greater than the pth percentile.
pth percentile
the 25th, 50th, and 75th percentiles, referred to as the first, second (median), and third quartile, respectively. the quartiles can be used to divide a data set into four parts, with each part containing approximately 25% of the data.
quartiles
a measure of variability, defined to be the largest value minus the smallest value.
range
a measure of variability, defined to be the difference between the third and first quartiles
interquartile range (IQR)
a measure of variability based on the squared deviations of the data values about the mean.
variance
a measure of variability computed by taking the positive square root of the variance.
standard deviation
a measure of relative variability computed by dividing the standard deviation by the mean and mulptiplying by 100
coefficient of variation
a measure of the shape of a data distribution. data skewed to the left=negative skewness. skewed to the right=positive skewness. symmetrical data=zero skewness
skewness
a value computed by dividing the deviation about the mean (xi-x bar) by the standard deviation s. a z-score is referred to as a standardized value and denotes the number of standard deviations xi is from the mean.
z-score
a theorem that can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean
chebyshev’s theorem
a rule that can be used to compute the percentage of data values that must be within one, two and three standard deviations of the mean for the data that exhibit a bell-shaped distribution.
emperical rule
an unusually small or large data value
outlier
a technique that uses 5 numbers to summarize the data: smallest value, 1st quartile, median, 3rd quartile, largest value
five number summary
a graphical summary of data based on a 5 number summary
box plot
a measure of linear association between two variables. positive values=positive relationship. negative values=negative relationship.
covariance
a measure of linear association between two variables that takes on values between -1 and +1. values near +1 indicate a strong positive linear relationship. values near -1 indicate a strong negative linear relationship. and values near zero lack any liner relationship.
correlation coefficient
