Chapter 3 Vocabulary

Mode

A measure of location, defined as the value that occurs with greatest frequency .

Coefficient of variation

A measure of relative variability computed by dividing the standard deviation by the mean and multiplying by 100.

Box Plot

A graphical summary of data based on a five-number summary.

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 computed by the value in the middle when the data are arranged in ascending order.

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 relationship; and values near zero indicate the lack of a linear relationship.

Covariance

A measure of linear association between two variables. Positive values indicate a positive relationship; negative value indicate a negative relationship.

Geometric Mean

A measure of location that is calculated by finding the nth root of the product of n values.

Skewness

A measure of the shape of a data distribution. Data skewed to the left result in negative skewness; a symmetric data distribution results in zero skewness; and data skewed to the right results in positive skewness.

Variance

A measure of variability based on the squared deviation of the data values about the mean

Standard Deviation

A measure of variability computed by the taking the positive square root of the variance.

Interquartile Range (IQR)

A measure of variability, defined to be the difference between the third and fourth quartiles.

Range

A measure of variability, defined to be the largest value minus the smallest value

Population Parameter

A numerical value used as a summary measure for a population (e.g., the population mean, the population variance, and the population standard deviation).

Sample Statistic

A numerical value used as a summary measure for a sample (e.g., the sample mean, the sample variance, and the sample standard deviation).

Empirical rule

A rule that can be used to compute the percentage of data values that must be within one, two, three standard deviations of the mean for data that exhibit a bell-shaped distribution.

Point Estimator

A sample statistic, such as the sample mean, the sample variance, and the sample standard deviation, used to estimate the corresponding population parameter.

Five-Number Summary

A technique that uses five numbers to summarize to summarize the data: smallest value, first quartile, median, third quartile, and largest value.

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

Z-Score

A value computed by dividing the deviation about the mean (xi-Sample mean) 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.

Percentile

A value such that at least p percent of the observations are less than or equal to this value and at least (100-p) percent of the observations are greater than or equal to this value. The 50th percentile is the median.

Outlier

An unusually small or unusually large data value.

Quartiles

The 25th, 50th, and 75th percentiles, referred to as the first quartile, second quartile (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.

Weighted mean

The mean obtained by assigning each observation a weight that reflects its importance.