BUSINESS DECISION MAKING. Topic 1 Introduction to Statistical Thinking and Business Decision Making Process; Data Collection and Presentation

Transcription

1 BUSINESS DECISION MAKING Topic 1 Introduction to Statistical Thinking and Business Decision Making Process; Data Collection and Presentation (Chap 1 The Nature of Probability and Statistics) (Chap 2 Frequency Distributions and Graphs) Bluman, Chapter 1 & 2 1

2 How is Statistics used in Business? To solve Business problems and make decisions, population censuses, opinion polls, consumer data bases, and sales and demand data are required to gather information about customers make sales forecasting do market research The role of the Statistician is to determine, for a given question, the type of data that is needed, the way it should be collected and how it should be analysed in order to best answer that question. Peter Chapter 1 2

3 Business Problem-Solving Process Business Question Define Objectives Review Past Data and Brainstorm Management Action Report & Present Interpret & Draw Conclusions Implement, monitor, more research Hypotheses to test Phrase as Statistical Question Analyse Data Peter Chapter 2 Collect Data (Qualitative/Quantitative) 3

4 Chapter 1 Overview Introduction 1-1 Descriptive and Inferential Statistics 1-2 Variables and Types of Data 1-3 Data Collection & Sampling Techniques 1-4 Experimental Designs 1-5 Computers and Calculators Bluman Chapter 1 4

5 Chapter 1 Objectives 1. Demonstrate knowledge of statistical terms. 2. Differentiate between the two branches of statistics. 3. Identify types of data. 4. Identify the measurement level for each variable. 5. Identify the four basic sampling techniques. Bluman, Chapter 1 5

6 Introduction Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. Bluman Chapter 1 6

7 1-1 Descriptive and Inferential Statistics A variable is a characteristic or attribute that can assume different values. The values that a variable can assume are called data. A population consists of all subjects (human or otherwise) that are studied. A sample is a subset of the population. Bluman Chapter 1 7

8 1-1 Descriptive and Inferential Statistics Descriptive statistics consists of the collection, organization, summarization, and presentation of data. Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions. Bluman Chapter 1 8

9 1-2 Variables and Types of Data Data Qualitative Categorical Quantitative Numerical, Can be ranked Discrete Countable 5, 29, 8000, etc. Continuous Can be decimals 2.59, 312.1, etc. Bluman Chapter 1 9

10 1-2 Recorded Values and Boundaries Variable Recorded Value Boundaries Length 15 centimeters (cm) Temperature 86 Fahrenheit ( F) Time 0.43 second (sec) Mass 1.6 grams (g) cm F sec g Bluman Chapter 1 10

11 1-2 Variables and Types of Data Levels of Measurement 1. Nominal categorical (names) 2. Ordinal nominal, plus can be ranked (order) 3. Interval ordinal, plus intervals are consistent 4. Ratio interval, plus ratios are consistent, true zero Bluman Chapter 1 11

12 1-2 Variables and Types of Data Determine the measurement level. Variable Nominal Ordinal Interval Ratio Level Hair Color Yes No Nominal Zip Code Yes No Nominal Letter Grade Yes Yes No Ordinal ACT Score Yes Yes Yes No Interval Height Yes Yes Yes Yes Ratio Age Yes Yes Yes Yes Ratio Temperature (F) Yes Yes Yes No Interval Bluman Chapter 1 12

13 1-3 Data Collection and Sampling Techniques Some Sampling Techniques Random random number generator Systematic every k th subject Stratified divide population into layers Cluster use intact groups Convenient mall surveys Bluman Chapter 1 13

14 1-3 Random Sampling Samples are selected by using chance methods or random numbers Every member of the population has the same chance of being selected Random samples can be chosen by mechanical means (like lotteries), or by computers generating random numbers Example: 30 random numbers (from 1 to 1,000)

15 1-3 Systematic Sampling The items or individuals of the population are arranged in some order. A random starting point is selected and then every kth member of the population is selected for the sample. Example: Sample 8 customers from a total of 64 First Group: randomly select 3 rd person, then 8 th person (k) after that. N = 64 n = 8 k = 8 15

16 1-3 Stratified Sampling Divide population into subgroups (called strata) according to some common characteristic Samples within the strata should be randomly selected Samples from subgroups are combined into one Population Divided into 4 strata Sample 16

17 1-3 Cluster Sampling Population is divided into several groups called clusters by some means such as geographical area, each representative of the population The clusters are randomly selected and all members of the selected clusters will be used as the subjects of the samples Population divided into 16 clusters. Randomly selected clusters for sample 17

18 1-3 Convenient Sampling Samples that are convenient to obtain are used Samples selected may or may not represent the population Researcher needs to investigate the characteristics of the population and determines that the sample is representative before using it Example: interview customers entering a mall to determine the nature of their visit 18

19 Chapter 2 Overview Introduction 2-1 Organizing Data 2-2 Histograms, Frequency Polygons, and Ogives 2-3 Other Types of Graphs 2-4 Paired Data and Scatter Plots 19

20 Chapter 2 Objectives 1. Organize data using frequency distributions. 2. Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives. 20

21 2-1 Organizing Data Data collected in original form is called raw data. A frequency distribution is the organization of raw data in table form, using classes and frequencies. Nominal- or ordinal-level data that can be placed in categories is organized in categorical frequency distributions. 21

22 Chapter 2 Frequency Distributions and Graphs Section 2-1 Example

23 Categorical Frequency Distribution Twenty-five army indicates were given a blood test to determine their blood type. Raw Data: A,B,B,AB,O O,O,B,AB,B B,B,O,A,O A,O,O,O,AB AB,A,O,B,A Construct a frequency distribution for the data. 23

24 Categorical Frequency Distribution Twenty-five army indicates were given a blood test to determine their blood type. Raw Data: A,B,B,AB,O O,O,B,AB,B B,B,O,A,O A,O,O,O,AB AB,A,O,B,A Class Tally Frequency Percent A IIII 5 20 B IIII II 7 28 O IIII IIII 9 36 AB IIII

25 Grouped Frequency Distribution Grouped frequency distributions are used when the range of the data is large. The smallest and largest possible data values in a class are the lower and upper class limits. Class boundaries separate the classes. To find a class boundary, average the upper class limit of one class and the lower class limit of the next class. 25

26 Grouped Frequency Distribution The class width can be calculated by subtracting successive lower class limits (or boundaries) successive upper class limits (or boundaries) upper and lower class boundaries The class midpoint X m can be calculated by averaging upper and lower class limits (or boundaries) 26

27 Rules for Classes in Grouped Frequency Distributions 1. There should be 5-20 classes. 2. The class width should be an odd number. 3. The classes must be mutually exclusive. 4. The classes must be continuous. 5. The classes must be exhaustive. 6. The classes must be equal in width (except in openended distributions). 27

28 Chapter 2 Frequency Distributions and Graphs Section 2-1 Example

29 Constructing a Grouped Frequency Distribution The following data represent the record high temperatures for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes

30 Constructing a Grouped Frequency Distribution STEP 1 Determine the classes. Find the class width by dividing the range by the number of classes 7. Range = High Low = = 34 Width = Range/7 = 34/7 = 5 Rounding Rule: Always round up if a remainder. 30

31 Constructing a Grouped Frequency Distribution For convenience sake, we will choose the lowest data value, 100, for the first lower class limit. The subsequent lower class limits are found by adding the width to the previous lower class limits. Class Limits The first upper class limit is one less than the next lower class limit. The subsequent upper class limits are found by adding the width to the previous upper class limits. 31

32 Constructing a Grouped Frequency Distribution The class boundary is midway between an upper class limit and a subsequent lower class limit. 104,104.5,105 Class Limits Class Boundaries Frequency Cumulative Frequency

33 Constructing a Grouped Frequency Distribution STEP 2 Tally the data. STEP 3 Find the frequencies. Class Limits Class Boundaries Frequency Cumulative Frequency

34 Constructing a Grouped Frequency Distribution STEP 4 Find the cumulative frequencies by keeping a running total of the frequencies. Class Limits Class Boundaries Frequency Cumulative Frequency

35 2-2 Histograms, Frequency Polygons, and Ogives 3 Most Common Graphs in Research 1. Histogram 2. Frequency Polygon 3. Cumulative Frequency Polygon (Ogive) 35

36 2-2 Histograms, Frequency Polygons, and Ogives The histogram is a graph that displays the data by using vertical bars of various heights to represent the frequencies of the classes. The class boundaries are represented on the horizontal axis. 36

37 Chapter 2 Frequency Distributions and Graphs Section 2-2 Example

38 Histograms Construct a histogram to represent the data for the record high temperatures for each of the 50 states (see Example 2 2 for the data). 38

39 Histograms Histograms use class boundaries and frequencies of the classes. Class Limits Class Boundaries Frequency

40 Histograms Histograms use class boundaries and frequencies of the classes. 40

41 2.2 Histograms, Frequency Polygons, and Ogives The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the class midpoints. The frequencies are represented by the heights of the points. The class midpoints are represented on the horizontal axis. 41

42 Chapter 2 Frequency Distributions and Graphs Section 2-2 Example

43 Frequency Polygons Construct a frequency polygon to represent the data for the record high temperatures for each of the 50 states (see Example 2 2 for the data). 43

44 Frequency Polygons Frequency polygons use class midpoints and frequencies of the classes. Class Limits Class Midpoints Frequency

45 Frequency Polygons Frequency polygons use class midpoints and frequencies of the classes. A frequency polygon is anchored on the x-axis before the first class and after the last class. 45

46 2.2 Histograms, Frequency Polygons, and Ogives The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution. The upper class boundaries are represented on the horizontal axis. 46

47 Chapter 2 Frequency Distributions and Graphs Section 2-2 Example

48 Ogives Construct an ogive to represent the data for the record high temperatures for each of the 50 states (see Example 2 2 for the data). 48

49 Ogives Ogives use upper class boundaries and cumulative frequencies of the classes. Class Limits Class Boundaries Frequency Cumulative Frequency

50 Ogives Ogives use upper class boundaries and cumulative frequencies of the classes. Class Boundaries Less than Less than Less than Less than Less than Less than Less than Cumulative Frequency

51 Ogives Ogives use upper class boundaries and cumulative frequencies of the classes. 51

52 Procedure Table Constructing Statistical Graphs 1: Draw and label the x and y axes. 2: Choose a suitable scale for the frequencies or cumulative frequencies, and label it on the y axis. 3: Represent the class boundaries for the histogram or ogive, or the midpoint for the frequency polygon, on the x axis. 4: Plot the points and then draw the bars or lines. 52

53 2.2 Histograms, Frequency Polygons, and Ogives If proportions are used instead of frequencies, the graphs are called relative frequency graphs. Relative frequency graphs are used when the proportion of data values that fall into a given class is more important than the actual number of data values that fall into that class. 53

54 Chapter 2 Frequency Distributions and Graphs Section 2-2 Example

55 Construct a histogram, frequency polygon, and ogive using relative frequencies for the distribution (shown here) of the miles that 20 randomly selected runners ran during a given week. Class Boundaries Frequency

56 Histograms The following is a frequency distribution of miles run per week by 20 selected runners. Class Boundaries Frequency Relative Frequency 1 1/20 = /20 = /20 = /20 = /20 = /20 = /20 = 0.10 Σf = 20 Σrf = 1.00 Divide each frequency by the total frequency to get the relative frequency. 56

57 Histograms Use the class boundaries and the relative frequencies of the classes. 57

58 Frequency Polygons The following is a frequency distribution of miles run per week by 20 selected runners. Class Boundaries Class Midpoints Relative Frequency

59 Frequency Polygons Use the class midpoints and the relative frequencies of the classes. 59

60 Ogives The following is a frequency distribution of miles run per week by 20 selected runners. Class Boundaries Frequency Cumulative Frequency Cum. Rel. Frequency Σf = /20 = 3/20 = 6/20 = 11/20 = 15/20 = 18/20 = 20/20 =

61 Ogives Ogives use upper class boundaries and cumulative frequencies of the classes. Class Boundaries Less than 10.5 Less than 15.5 Less than 20.5 Less than 25.5 Less than 30.5 Less than 35.5 Less than 40.5 Cum. Rel. Frequency

62 Ogives Use the upper class boundaries and the cumulative relative frequencies. 62

63 Shapes of Distributions 63

64 Shapes of Distributions 64