Chapter 1 Data and Statistics Statistics The art and science of collecting analyzing presenting and interpreting data Data The facts and figures collected analyzed and summarized for presentation and interpretation Data set All the data collected in a particular study Elements The entities on which data are collected Variable A characteristic of interest for the elements Observation The set of measurements obtained for a particular element Nominal scale The scale of measurement for a variable when the data are labels or names used to identify an attribute of an element Nominal data may be nonnumeric or numeric Ordinal scale The scale of measurement for a variable if the data exhibit the properties of nominal data and the order or rank of the data is meaningful Ordinal data may be nonnumeric or numeric Interval scale The scale of measurement for a variable if the data demonstrate the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure Interval data are always numeric Ratio scale The scale of measurement for a variable if the data demonstrate all the properties of interval data and the ratio of two values is meaningful Ratio data are always numeric Categorical data Labels or names used to identify an attribute of each element Categorical data use either the nominal or ordinal scale of measurement and may be nonnumeric or numeric Quantitative data Numeric values that indicate how much or how many of something Quantitative data are obtained using either the interval or ratio scale of measurement Categorical variable A variable with categorical data Quantitative variable A variable with quantitative data Cross sectional data Data collected at the same or approximately the same point in time Time series data Data collected over several time periods Descriptive statistics Tabular graphical and numerical summaries of data Population The set of all elements of interest in a particular study Sample A subset of the population Census A survey to collect data on the entire population Sample survey A survey to collect data on a sample Statistical inference The process of using data obtained from a sample to make estimates or test hypotheses about the characteristics of a population Data mining The process of using procedures from statistics and computer science to extract useful information from extremely large databases Chapter 2 Descriptive Statistics Tabular and Graphical Presentations Bar Chart Frequency FREQUENCY DISTRIBUTION OF SOFT DRINK PURCHASES Soft Drink Coke Classic 19 8 Diet Coke 5 Dr Pepper 13 Pepsi 5 Sprite 50 Total Pie Chart RELATIVE FREQUENCY AND PERCENT FREQUENCY DISTRIBUTIONS FOR THE AUDIT TIME DATA Dot Plot Histogram Ogive TYPES OF RELATIONSHIPS DEPICTED BY SCATTER DIAGRAMS Categorical data Labels or names used to identify categories of like items Quantitative data Numerical values that indicate how much or how many Frequency distribution A tabular summary of data showing the number frequency of data values in each of several nonoverlapping classes Relative frequency distribution A tabular summary of data showing the fraction or proportion of data values in each of several nonoverlapping classes Percent frequency distribution A tabular summary of data showing the percentage of data values in each of several nonoverlapping classes Bar chart A graphical device for depicting qualitative data that have been summarized in a frequency relative frequency or percent frequency distribution Pie chart A graphical device for presenting data summaries based on subdivision of a circle into sectors that correspond to the relative frequency for each class Class midpoint The value halfway between the lower and upper class limits Dot plot A graphical device that summarizes data by the number of dots above each data value on the horizontal axis Histogram A graphical presentation of a frequency distribution relative frequency distribution or percent frequency distribution of quantitative data constructed by placing the class intervals on the horizontal axis and the frequencies relative frequencies or percent frequencies on the vertical axis Cumulative frequency distribution A tabular summary of quantitative data showing the number of data values that are less than or equal to the upper class limit of each class Cumulative relative frequency distribution A tabular summary of quantitative data showing the fraction or proportion of data values that are less than or equal to the upper class limit of each class Cumulative percent frequency distribution A tabular summary of quantitative data showing the percentage of data values that are less than or equal to the upper class limit of each class Ogive A graph of a cumulative distribution Exploratory data analysis Methods that use simple arithmetic and easy to draw graphs to summarize data quickly Stem and leaf display An exploratory data analysis technique that simultaneously rank orders quantitative data and provides insight about the shape of the distribution Crosstabulation A tabular summary of data for two variables The classes for one variable are represented by the rows the classes for the other variable are represented by the columns Simpson s paradox Conclusions drawn from two or more separate crosstabulations that can be reversed when the data are aggregated into a single crosstabulation Scatter diagram A graphical presentation of the relationship between two quantitative variables One variable is shown on the horizontal axis and the other variable is shown on the vertical axis Trendline A line that provides an approximation of the relationship between two variables Approximate Class Width Largest data value Smallest data value Number of classes Relative Frequency Frequency of the class n Chapter 3 Descriptive Statistics Numerical Measures Sample statistic A numerical value used as a summary measure for a sample e g the sample mean the sample variance s2 and the sample standard deviation s Population parameter A numerical value used as a summary measure for a population e g the population mean the population variance 2 and the population standard deviation Point estimator The sample statistic such as s2 and s when 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