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Math 102- Statistics

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Zahra Zulaikha
Zahra Zulaikha

Dec 15, 2011 with Ma'am Daisy

EducationTechnologyEconomy & Finance
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INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE Teaching Basic Statistics
Session 1. TEACHING BASIC STATISTICS
Realities about Statistics ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Definition of Statistics ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
History of Statistics ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Application of Statistics ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Application of Statistics ,[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Two Aims of Statistics ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Areas of Statistics ,[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Examples of Descriptive Statistics ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Examples of Inferential Statistics ,[object Object],Session 1. TEACHING BASIC STATISTICS
Inferential Statistics Session 1. TEACHING BASIC STATISTICS Larger Set ( N units/observations) Smaller Set ( n units/observations ) Inferences and Generalizations
Key Definitions ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Key Definitions ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Types of Variables ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Levels of Measurement ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Session 1. TEACHING BASIC STATISTICS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Session 1. TEACHING BASIC STATISTICS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Session 1. TEACHING BASIC STATISTICS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Session 1. TEACHING BASIC STATISTICS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Methods of Presenting Data ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Session 1. TEACHING BASIC STATISTICS Mean Median Mode Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range Location Maximum Minimum Central Tendency Percentile Quartile Decile Interquartile Range Skewness Kurtosis
Measures of Location ,[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Maximum and Minimum ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Measure of Central Tendency ,[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Mean ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS Sample Mean Population Mean
Properties of the Mean ,[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Properties of the Mean ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 6 Mean = 5
Median ,[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Properties of a Median ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5
Mode ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 0 1 2 3 4 5 6 No Mode
Properties of a Mode ,[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Mean, Median & Mode ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Mean, Median & Mode ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Mean, Median & Mode ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Percentiles ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
EXAMPLE ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Deciles ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Quartiles ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Measures of Variation ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Session 1. TEACHING BASIC STATISTICS Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C A look at dispersion…
Two Types of Measures of Dispersion ,[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS Relative Measure of Dispersion:  Coefficient of Variation
Range (R) Session 1. TEACHING BASIC STATISTICS The difference between the maximum and minimum value in a data set, i.e. R = MAX – MIN Example: Pulse rates of 15 male residents of a certain village 54 58 58 60 62 65 66 71 74 75 77 78 80 82 85 R = 85 - 54 = 31
Some Properties of the Range ,[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Inter-Quartile Range (IQR) Session 1. TEACHING BASIC STATISTICS The difference between the third quartile and first quartile, i.e. IQR = Q 3 – Q 1 Example: Pulse rates of 15 residents of a certain village 54 58 58 60 62 65 66 71 74 75 77 78 80 82 85 IQR = 78 - 60 = 18
Some Properties of IQR ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Variance ,[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Standard Deviation (SD) ,[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Session 1. TEACHING BASIC STATISTICS Data: 10 12 14 15 17 18 18 24 n = 8 Mean =16 Computation of Standard Deviation
Session 1. TEACHING BASIC STATISTICS Remarks on Standard Deviation ,[object Object],[object Object]
Comparing Standard Deviation Session 1. TEACHING BASIC STATISTICS Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C
Comparing Standard Deviation Session 1. TEACHING BASIC STATISTICS Example: Team A - Heights of five marathon players in inches 65” 65 “ 65 “ 65 “ 65 “ 65 “ Mean = 65 S = 0
Comparing Standard Deviation Session 1. TEACHING BASIC STATISTICS Example: Team B - Heights of five marathon players in inches 62 “ 67 “ 66 “ 70 “ 60 “ Mean = 65” s = 4.0”
Properties of Standard Deviation ,[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Coefficient of Variation (CV) ,[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Comparing CVs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Measure of Skewness ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
What is Symmetry? ,[object Object],Session 1. TEACHING BASIC STATISTICS
[object Object],Measure of Skewness ,[object Object],Session 1. TEACHING BASIC STATISTICS
Measure of Kurtosis ,[object Object],[object Object],Session 1. TEACHING BASIC STATISTICS
Measure of Kurtosis Session 1. TEACHING BASIC STATISTICS K = 0 mesokurtic K > 0 leptokurtic K < 0 platykurtic

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Math 102- Statistics

  • 1. INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE Teaching Basic Statistics
  • 2. Session 1. TEACHING BASIC STATISTICS
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  • 12. Inferential Statistics Session 1. TEACHING BASIC STATISTICS Larger Set ( N units/observations) Smaller Set ( n units/observations ) Inferences and Generalizations
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  • 22. Session 1. TEACHING BASIC STATISTICS Mean Median Mode Summary Measures Variation Variance Standard Deviation Coefficient of Variation Range Location Maximum Minimum Central Tendency Percentile Quartile Decile Interquartile Range Skewness Kurtosis
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  • 41. Session 1. TEACHING BASIC STATISTICS Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C A look at dispersion…
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  • 43. Range (R) Session 1. TEACHING BASIC STATISTICS The difference between the maximum and minimum value in a data set, i.e. R = MAX – MIN Example: Pulse rates of 15 male residents of a certain village 54 58 58 60 62 65 66 71 74 75 77 78 80 82 85 R = 85 - 54 = 31
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  • 45. Inter-Quartile Range (IQR) Session 1. TEACHING BASIC STATISTICS The difference between the third quartile and first quartile, i.e. IQR = Q 3 – Q 1 Example: Pulse rates of 15 residents of a certain village 54 58 58 60 62 65 66 71 74 75 77 78 80 82 85 IQR = 78 - 60 = 18
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  • 49. Session 1. TEACHING BASIC STATISTICS Data: 10 12 14 15 17 18 18 24 n = 8 Mean =16 Computation of Standard Deviation
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  • 51. Comparing Standard Deviation Session 1. TEACHING BASIC STATISTICS Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = .9258 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.57 Data C
  • 52. Comparing Standard Deviation Session 1. TEACHING BASIC STATISTICS Example: Team A - Heights of five marathon players in inches 65” 65 “ 65 “ 65 “ 65 “ 65 “ Mean = 65 S = 0
  • 53. Comparing Standard Deviation Session 1. TEACHING BASIC STATISTICS Example: Team B - Heights of five marathon players in inches 62 “ 67 “ 66 “ 70 “ 60 “ Mean = 65” s = 4.0”
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  • 61. Measure of Kurtosis Session 1. TEACHING BASIC STATISTICS K = 0 mesokurtic K > 0 leptokurtic K < 0 platykurtic