# Basic statistics collected lectures Chipeva

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CONTENTS
I. INTRODUCTION 5

1. Some historical notes 5

2. Application of Statistics . 6

3. Object of Statistics 7

4. Subject of Statistics —7

5. Basic Statistical Definitions and Concepts 8

II. STATISTICAL RESEARCH... 14

III. SURVEY AND REGISTRATION OF PRIMARY DATA.. 19

1. Preparation of Statistical Research 19

2. Primary Statistical Table . 20

3. Survey 21

4. Errors in Statistical Research . 22

IV. DATA PRESENTATION .24

1. Data Grouping 24

2. Classifications of statistical groupings 25

3. Grouping procedure for Univariate grouping . 27

4. Table of frequency distribution : ; 36

5. Graphs and charts of frequency distributions. . 37

V. STATISTICS OF UNIVARIATE FREQUENCY DISTRIBUTIONS 41

1. Univariate Frequency Distribution....' ...;. . 41

2. Classification of frequency distributions .... 42

3. Statistics of univariate frequency distributions 44

VI. MEASURES OF CENTRAL TENDENCY y. 46

1. Arithmetic mean 47

2. Median 54

3. Mode : 58

VII. STATISTICAL VARIATION   61

1. Absolute measures of variation. 61

2. Relative measures of Variation 63

3. Interpretation of the measures of variation 70

VIII. SHAPE OF FREQUENCY DISTRIBUTION -

SKEWNESS AND KIRTOSIS ..74

1. Measures of skewness 74

2. Measures of kurtosis .....: 78

3. Relation between measures of central tendency in a frequency distribution.......80

IX. STATISTICAL ENFERENCE...    82

1. Basic concepts and definitions in the probability theory 82

2. Univariate probability distributions 89

3. Theoretical base of the statistical inference 95

4. Sampling 97

5. Random sample 98

X. PARAMETER ESTIMATION    101

1. Principal concepts and definitions 101

2. Errors of parameter-estimates 102

3. Point estimates of mean, variance and proportion 103

4. Sample distribution and standard error of mean and proportion . 105

5- Interval estimates of mean and proportion 108

6. Sample size for interval estimate of the mean and the proportion 112

XI. HYPOTHESIS TESTING 115

1. Basic concepts and definitions 116

2. Formal steps of hypothesis testing 123

XII. HYPOTHESIS TESTING ABOUT POPULATION MEANS AND

PROPORTIONS   125

1. Hypothesis testing about one population mean or proportion 125

2. Hypothesis testing about the difference between two population means

or proportion 133

XIII. STATISTICAL STUDY OF RELATIONSHIPS    ...147

XIV. ANALYSIS OF VARIANCE   150

1. Concepts, classifications and requirements of application : 150

2. One-way ANOVA procedure .... 152

XV. REGRESSION ANALYSIS 161

1. Basic concepts and definitions 161

2. Procedure of simple regression analysis . 163

3. Parameters estimation in a regression model 167

4. Complementary procedures in regression analysis. 169

5. Simple linear regression model 170

XVI. SINGLE CORRELATION COEFFICIENTS AND SOME OTHER

COEEFICIENTS OF RELATIONSHIP   175

1. Pearson’s correlation coefficient   175

2. Brave’s correlation coefficient (linear correlation coefficient) .....176

3. Coefficient of determination 177

4. Coefficient of indemoni nation 177

XVII. TIME SERIES ANALYSIS   178

1. Introduction. 178

2. Elementary measures for time series movements 179

3. Components of time series 183

4. Statistical analysis of trend 188

5. Linear Trend Model 192

6. Analysis of the seasonal component 196

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