Chapter One What is Statistics? 1.1 What is Statistics? “Statistics is a way to get information from data” Statistics Data Information Statistics is a tool for creating new understanding from a set of numbers Definitions: Oxford English Dictionary Copyright © 2009 Cengage Learning 1.2 Descriptive Statistics Descriptive statistics deals with methods of organizing, summarizing, and presenting data in a convenient and informative way. One form of descriptive statistics uses graphical techniques Copyright © 2009 Cengage Learning 1.3 Descriptive Statistics Another form of descriptive statistics uses numerical techniques to summarize data. The mean and median are popular numerical techniques to describe the location of the data. The range, variance, and standard deviation measure the variability of the data Copyright © 2009 Cengage Learning 1.4 Inferential statistics Inferential statistics is a body of methods used to draw conclusions or inferences about characteristics of populations based on sample data. Copyright © 2009 Cengage Learning 1.5 Key Statistical Concepts Population — a population is the group of all items of interest to a statistics practitioner — frequently very large; sometimes infinite E.g. All the population in Vietnam Sample — A sample is a set of data randomly drawn from the population — Potentially large, but less than the population E.g. A sample of citizens living in Hanoi Copyright © 2009 Cengage Learning 1.6 Key Statistical Concepts Parameter — A descriptive measure of a population Statistic — A descriptive measure of a sample Copyright © 2009 Cengage Learning 1.7 Key Statistical Concepts Population Sample Subset Parameter Statistic Populations have Parameters, Samples have Statistics Copyright © 2009 Cengage Learning 1.8 Statistical Inference Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample Population Sample Inference Statistic Parameter What can we infer about a Population’s Parameters based on a Sample’s Statistics? Copyright © 2009 Cengage Learning 1.9 Chapter Two Graphical and Tabular Descriptive Techniques 2.10 32 Shapes of Histograms… Modality A unimodal histogram: a single peak, A bimodal histogram: two peaks: Bimodal Frequency Frequency Unimodal Variable Variable A modal class Copyright © 2009 Cengage Learning 33 Shapes of Histograms… Frequency A special type of symmetric unimodal histogram is one that is bell shaped: Variable Bell Shaped Copyright © 2009 Cengage Learning 34 Stem & Leaf Display… • Retains information about individual observations that would normally be lost in the creation of a histogram • Split each observation into two parts, a stem and a leaf: • e.g. Observation value: 42.19 • There are several ways to split it up… • We could split it at the decimal point: Stem Leaf 42 19 • Or split it at the “tens” position (while rounding to the nearest integer in the “ones” position) Copyright © 2009 Cengage Learning 35 Stem & Leaf Display… • Use the “stems” for the classes • Each leaf becomes part of the histogram Stem Leaf 0000000000111112222223333345555556666666778888999999 000001111233333334455555667889999 0000111112344666778999 001335589 124445589 33566 3458 022224556789 Thus, we still have access to our 334457889999 00112222233344555999 original data point’s value! 10 001344446699 11 124557889 Copyright © 2009 Cengage Learning 36 Histogram and Stem & Leaf… Compare the overall shapes of the figures… Copyright © 2009 Cengage Learning 37 Ogive (pronouncedOhưjive) agraphofacumulativefrequencydistribution RelativeFrequency=#ofobservationsinaclass Total#ofobservations Copyright â 2009 Cengage Learning 38 Relative Frequencies… Copyright © 2009 Cengage Learning 39 Cumulative Relative Frequencies… Cumulative relative frequencies = the current class’ relative frequency + the previous class’ cumulative relative frequency first class… next class: .355+.185=.540 : : last class: .930+.070=1.00 Copyright © 2009 Cengage Learning 40 Ogive… Graph the cumulative relative frequencies… Copyright © 2009 Cengage Learning 41 Ogive… The ogive can be used to answer questions like: What value is at the 50th percentile? “around $35” Copyright © 2009 Cengage Learning (Refer also to Fig. 2.13 in your textbook) 42 Describing Time Series Data Observations measured at successive points in time are called timeseries data Line chart plots the value of the variable on the vertical axis against time periods on the horizontal axis Copyright © 2009 Cengage Learning 43 the monthly average retail price of gasoline Copyright © 2009 Cengage Learning 44 Price of Gasoline in 1982-84 Constant Dollars Copyright © 2009 Cengage Learning 45 Summary I… Factors That Identify When to Use Frequency and Relative Frequency Tables, Bar and Pie Charts 1. Objective: Describe a single set of data 2. Data type: Nominal Factors That Identify When to Use a Histogram, Ogive, or StemandLeaf Display 1. Objective: Describe a single set of data 2. Data type: Interval Factors that Identify When to Use a Crossclassification Table 1. Objective: Describe the relationship between two variables 2. Data type: Nominal Factors that Identify When to Use a Scatter Diagram 1. Objective: Describe the relationship between two variables 2. Data type: Interval Copyright © 2009 Cengage Learning 46 Summary II… Interval Data Histogram Single Set of Data Relationship Between Two Variables Copyright © 2009 Cengage Learning Scatter Diagram Nominal Data Frequency and Relative Frequency Tables, Bar and Pie Charts Bar Charts ... Descriptive statistics deals with methods of organizing, summarizing, and presenting data in a convenient and informative way. One form of descriptive statistics uses graphical techniques Copyright © 2009 Cengage Learning 1.3 Descriptive Statistics... Another form of descriptive statistics uses numerical techniques to summarize data. The mean and median are popular numerical techniques to describe the location of the data. The range, variance, and standard deviation measure the ... based on a Sample’s Statistics? Copyright © 2009 Cengage Learning 1.9 Chapter Two Graphical and Tabular Descriptive Techniques 2.10 11 Definitions… A variable is some characteristic of a population or sample