1-Review of Basic Statistical Concepts.docx - CHAPTER 1 REVIEW OF BASIC STATISTICS CONCEPTS 1 2 3 4 5 6 Rules of Summation What is Statistics 2.1

# 1-Review of Basic Statistical Concepts.docx - CHAPTER 1...

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CHAPTER 1 REVIEW OF BASIC STATISTICS CONCEPTS 1. Rules of Summation 2. What is Statistics? 2.1. Descriptive statistics 2.2. Inferential statistics 2.2.1. population 2.2.2. Sample 3. Important Measures of Central Tendency and Data Variability 3.1. The Mean 3.1.1. population mean µ 3.1.2. sample mean 3.2. The Mean as the Center of Gravity of the Data 3.3. Variance 3.3.1. Variance of Population Data 3.3.2. Sample Variance 3.4. Standard Deviation 3.5. The z -score 4. Measures of Association Between Two Variables 4.1. Covariance 4.1.1. Population Covariance 4.1.1.1. Covariance is affected by the scale of the data 4.1.1.2. The covariance sign (−, +) indicates the direction of relationship between x and y 4.1.1.3. When x and y are Unrelated 4.1.1.4. The Computational (Simpler) Formula for Covariance 4.1.2. Sample Covariance 4.2. Correlation Coefficient 5. Random Variables 5.1. Probability Distribution (Probability Density Function) of Discrete Random Variables 5.2. Expected Value of Discrete Random Variables 5.2.1. Expected Value Rules 5.3. Variance of the Discrete Random Variable 5.3.1. Variance Rules 5.4. The Fixed and Random Components of a Random Variable 5.5. Joint Probability Distribution (Probability Density Function) of Two Random Variables 5.6. Independent versus Dependent Random Variables 5.7. Covariance of x and y 5.7.1. The covariance formula simplified 5.8. Coefficient of Correlation 5.9. Effect of Linear Transformation of Two Random Variables on Their Covariance and Correlation 5.10.The Mean and Variance of the Sum of Two Random Variables 6. Normal Distribution 1-Numerical Descriptive Statistics 1 of 39
1. Rules of Summation 1) Sum of x i . i = 1 n x i = x 1 + x 2 + + x n i x i 1 20 2 21 3 19 4 22 5 24 106 i = 1 5 x i = 20 + 21 + 19 + 22 + 24 = 106 2) For a given constant k . i = 1 n k = k + k + + k = nk i = 1 5 10 = 10 + 10 + 10 + 10 + 10 i = 1 5 10 = 5 × 10 = 50 3) Sum of k x i i = 1 n k x i = k x 1 + k x 2 + + k x n i = 1 n k x i = k ( x 1 + x 2 + + x n ) i = 1 n k x i = k i = 1 n x i 4) Sum of k + m x i i = 1 n ( k + m x i )= ( k + m x 1 ) + ( k + m x 2 ) + + ( k + m x n ) i = 1 n ( k + m x i )= ( k + k + k ) + m ( x 1 + x 2 + x n ) i = 1 n ( k + m x i )= i = 1 n k + m i = 1 n x i 1-Numerical Descriptive Statistics 2 of 39
i = 1 n ( k + m x i )= nk + m i = 1 n x i 5) Sum of x i + y i i = 1 n ( x i + y i )= ( x 1 + x 2 + x n ) + ( y 1 + y 2 + y n ) i = 1 n ( x i + y i )= i = 1 n x i + i = 1 n y i 2. What is Statistics? Statistics is a discipline which studies the collection, organization, presentation, analysis and interpretation of numerical data. There are two types of statistics: the descriptive statistics, and the inferential statistics. 2.1. Descriptive statistics Descriptive statistics is the easy part. It deals with the collection, organization, and presentation of data. Descriptive statistics involves tables, charts, and presentation of summary characteristics of the data, which include concepts such as the mean, median or standard deviation. Descriptive statistics is encountered daily in the news media. For example, in the weather report you frequently hear about the average temperature, precipitation, pollen count, etc., in a given month of the year. Or you may read about the stock market trend,

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