The Nature of Probability and Statistics

1. The Nature of Probability and Statistics Chapter 1 Sections 1 and 2 Pg 2-8

2. Learning Intentions • Classify each variable as qualitative or quantitative. • Decide whether descriptive or inferential statistics has been used in each scenario. • Decide whether each statement describes a population or a sample.

3. Key Terms • Statistics • Variable • Random Variable • Data • Data set • Data value • Descriptive statistics • Inferential statistics • Population • Sample • Qualitative Variables • Quantitative Variables • Discrete variables • Continuous variables

4. Statistics • Is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data

5. Descriptive and Inferential Statistics • Variable- is a characteristic that can assume different values • Data- are values that the variables can assume • Random variables- variables that are determined by chance

6. Data set- a collection of data values forms • Data value- each value in a data set

7. Descriptive and Inferential Statistics • Statistics can be divided into two main areas • Descriptive statistics • Inferential statistics

8. Descriptive Statistics • Consists of the collection, organization, summarization, and presentation of data • In this area the statistician tries to describe the situation. • Example: the national census, the results from the census give you the average age, income, and other facts

9. Inferential Statistics • Consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variable, and making predictions • Statistician tries to make inferences from samples to population • Uses probability (the chance of an event occurring) • Examples: playing cards, lottery, dice, bingo

10. Population and Sample • Population- consists of all subjects (human or otherwise) that are being studied. • Due size, income, etc. it is not possible to use population for statistical study • Sample- is a group of subjects selected from a population • Should have the same characteristics as the subjects in the population

11. Variables and Types of Data • Qualitative variable- variables that can be placed into distinct categories, according to some characteristic or attribute • Examples: gender, religious preference, geography • Quantitative variable- are numerical and can be ordered or ranked • Example: age, height, weight

12. Quantitative Variables • Discrete variable- assume values that can be counted • Example: number of children, students in a classroom, calls made • Continuous variable- can assume an infinite number of values between any two specific values. They are obtained by measuring. They often include fractions and decimals • Example: temperature, length, time, mass

13. Continuous Variables • Since the data is measured, answers must be rounded • Boundaries are written for convenience • Boundaries of a continuous variable are given in one additional decimal place and always end with the digit 5

14. Boundaries • Variable Recorded Value Boundaries • Length 15 cm 14.5-15.5cm • Temperature 86° Fahrenheit 85.5-86.5° F • Time 0.43 sec 0.425-0.435 sec • Mass 1.6 grams 1.55-1.65 g