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...

This preview shows page 1 - 4 out of 39 pages.

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
Image of page 1
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
Image of page 2
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,
Image of page 3
Image of page 4

You've reached the end of your free preview.

Want to read all 39 pages?

  • Fall '08
  • STAFF

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors