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Course review, syllabus, etc. Chapter 1 – Introduction Chapter 2 – Graphical Techniques

Quantitative Business Methods A First Course. Course review, syllabus, etc. Chapter 1 – Introduction Chapter 2 – Graphical Techniques. 3-21-05. Population and Sample. Population. Sample. Use statistics to summarize features. Use parameters to summarize features.

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Course review, syllabus, etc. Chapter 1 – Introduction Chapter 2 – Graphical Techniques

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  1. Quantitative Business Methods A First Course • Course review, syllabus, etc. • Chapter 1 – Introduction • Chapter 2 – Graphical Techniques 3-21-05

  2. Population and Sample Population Sample Use statistics to summarize features Use parameters to summarize features Inference on the population from the sample

  3. Some Important Definitions…… • A ___________________(or universe) is the whole collection of things under consideration. • A ______________ is a portion of the population selected for analysis. • A PARAMETER is a summary measure computed to describe a characteristic of the population.  µ • A STATISTIC is a summary measure computed to describe a characteristic of the sample.  •  Discuss examples……..Ω

  4. Statistical Methods • Descriptive Statistics • Inferential Statistics Collecting and describing data. Drawing conclusions and/or making decisions concerning a population based only on sample data.

  5. Descriptive Statistics • Collect Data • e.g. Survey • Present Data • e.g. Tables and graphs • Characterize Data • e.g. Sample Mean =

  6. Inferential Statistics • Estimatione.g. Estimate the population mean using the sample mean. • Hypothesis Testinge.g. Test the claim that the population mean weight is 120 pounds. Drawing conclusion and/or making decisions concerning a population based on sample results.

  7. Analytical Skills Inventory Exercise 1. Write the following in scientific notation (ex. 4.63 x 102 or 4.63E02) (you may use as many significant figures as you wish) A. 3864159831.025 B. 0.0000062514836 2. Write the following numbers in standard notation (ie. Not in scientific notation) A. 4.3650217E10 B. 2.1097326 x 10 -6 3. Perform the following calculations, using only your calculator (try to enter it all in to your calculator). 4. Perform the following calculation without using your calculator.

  8. Use the following information for problems 5-9. = 4.6 n = 10

  9. 1. A. 3.864159831025 x 109 or 3.864E09 B. 6.2514836 x 10-6 or 6.251E-06 2. A. 43650217000 B. 0.0000021097326 3. A. 9 B. 10 4. 10 5. 46 6. 274 7. 2116 8. 41.4 9. 0

  10. Chapter 2 Graphical Descriptive Techniques

  11. 2.1 Introduction • Descriptive statistics involves the arrangement, summary, and presentation of data, to enable meaningful interpretation, and to support decision making. • Descriptive statistics methods make use of • graphical techniques • numerical descriptive measures. • The methods presented apply to both • the entire population • the population sample

  12. 2.2 Types of data and information • A variable - a characteristic of population or sample that is of interest for us. • Cereal choice • Capital expenditure • The waiting time for medical services • Data - the actual values of variables • Interval data are numerical observations • Nominal data are categorical observations

  13. Types of data - examples Interval data Nominal Age - income 55 75000 42 68000 . . . . PersonMarital status 1 married 2 single 3 single . . . . Weight gain +10 +5 . . Computer Brand 1 IBM 2 Dell 3 IBM . . . .

  14. Types of data - examples Interval data Nominal data With nominal data, all we can do is, calculate the proportion of data that falls into each category. Age - income 55 75000 42 68000 . . . . Weight gain +10 +5 . . IBM Dell Compaq Other Total 25 11 8 6 50 50% 22% 16% 12%

  15. 2.3 Graphical Techniques for Interval Data • Example 2.1: The monthly bills of new subscribers in the first month after signing on with a telephone company. • Collect data • Prepare a frequency distribution • Draw a histogram

  16. Class width = [Range] / [# of classes] [119.63 - 0] / [8] = 14.95 15 Example 2.1: Providing information Collect data Prepare a frequency distribution How many classes to use? Number of observations Number of classes Less then 50 5-7 50 - 200 7-9 200 - 500 9-10 500 - 1,000 10-11 1,000 – 5,000 11-13 5,000- 50,000 13-17 More than 50,000 17-20 (There are 200 data points _______ observation _________ observation Largest observation Largest observation Largest observation Smallest observation Smallest observation Smallest observation

  17. Draw a Histogram Example 2.1: Providing information

  18. Example 2.1: Providing information What information can we extract from this histogram Relatively, large number of large bills About half of all the bills are small A few bills are in the middle range 71+37=108 13+9+10=32 80 18+28+14=60 60 Frequency 40 20 0 15 45 75 30 60 90 105 120 Bills

  19. Class frequency Total number of observations Class relative frequency = Relative frequency • It is often preferable to show the relative frequency (proportion) of observations falling into each class, rather than the frequency itself. • Relative frequencies should be used when • the population relative frequencies are studied • comparing two or more histograms • the number of observations of the samples studied are different

  20. Shapes of histograms Symmetry • There are four typical shape characteristics

  21. Shapes of histograms Skewness Negatively skewed ______________ skewed

  22. Modal classes A modal class is the one with the largest number of observations. A unimodal histogram The modal class

  23. Modal classes A bimodal histogram A modal class A modal class

  24. Bell shaped histograms “________________________”

  25. Interpreting histograms • Example 2.3: Comparing students’ performance • Students’ performance in two statistics classes. • Different in their teaching emphasis • Class A – math analysis and development of theory. • Class B – applications and computer based analysis. • The final mark was recorded. • Draw histograms and interpret the results.

  26. Interpreting histograms The mathematical emphasis creates two groups, and a larger spread.

  27. Observation: Stem Leaf 42 19 Stem Leaf 4 2 Stem and Leaf Display • Preliminary analysis. • Original observations vs. histogram approach. • Split each observation into two parts. • There are several ways of doing that: 42.19 42.19 A stem and leaf display forExample 2.1 will use thismethod 

  28. Stem and Leaf Display SG Demo A stem and leaf display for Example 2.1 (See page 42 for ref) Stem-and-Leaf Display for Bills: unit = 1.0 1|2 represents 12.0 52 0|0000000001111122222233333455555566666667788889999999 85 1|000001111233333334455555667889999 (23) 2|00001111123446667789999 92 3|001335589 83 4|12445589 75 5|33566 70 6|3458 66 7|022224556789 54 8|334457889999 42 9|00112222233344555999 22 10|001344446699 10 11|0124557889 The length of each linerepresents the _________ of the class defined by the stem.

  29. 1.000 .930 .790 .700 .650 60 75 90 105 120 Ogives SG Demo: Freq Tab Ogives are cumulative relative frequency distributions. Example 2.1 - continued } } .605 .540 .355 15 30 45

  30. 2.4 Graphical Techniques for Nominal data • The only allowable calculation on nominal data is to count the frequency of each value of a variable. • When the raw data can be naturally categorized in a meaningful manner, we can display frequencies by • Bar charts – emphasize frequency of occurrences of the different categories. • Pie chart – emphasize the proportion of occurrences of each category.

  31. The Pie Chart Ex #2.4: The student placement office at a university wanted to determine the general areas of employment of last year school graduates. Other 11.1% (28.9 /100)(3600) = 1040 Accounting 28.9% General management 14.2% Marketing 25.3% Finance 20.6%

  32. The Bar Chart • Rectangles represent each category. • The height of the rectangle represents the frequency. • The base of the rectangle is arbitrary SG Demo: Desc-Categ-Tab 73 64 52 36 28

  33. 2.5 Describing the Relationship Between Two Variables • The relationship between two interval variables. • Example 2.7 • A real estate agent wants to study the relationship between house price and house size • Twelve houses recently sold are sampled and the size and price recorded • Use graphical technique to describe the relationship between size and price. • SizePrice • 315 • 229 • 335 • 261 • …………….. • ……………..

  34. 2.5 Describing the Relationship Between Two Variables • Solution • The size (independent variable, X) affects the price (dependent variable, Y) • We use Excel to create a scatter diagram Y The greater the house size, the greater the price X

  35. Typical Patterns of Scatter Diagrams Negative linear relationship Positive linear relationship No relationship Negative nonlinear relationship Nonlinear (concave) relationship This is a weak linear relationship.A non linear relationship seems to fit the data better.

  36. Graphing the Relationship Between Two Nominal Variables • We create a contingency table. • This table lists the frequency for each combination of values of the two variables. • We can create a bar chart that represent the frequency of occurrence of each combination of values.

  37. Contingency table • Example 2.8(Data: 2.8a) • To conduct an efficient advertisement campaign the relationship between occupation and newspapers readership is studied. The following table was created

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