ppt01. A review to statistics and probability.pptx

Statistics and Probability

1. REVIEW TO STATISTICS

2. Variable A variable is a characteristic or condition that can change or take on different values. Most research begins with a general question about the relationship between two variables for a specific group of individuals.

3. Population The entire group of individuals is called the population. For example, a researcher may be interested in the relation between class size (variable 1) and academic performance (variable 2) for the population of third-grade children.

4. Sample Usually populations are so large that a researcher cannot examine the entire group. Therefore, a sample is selected to represent the population in a research study. The goal is to use the results obtained from the sample to help answer questions about the population.

5. Descriptive Statistics Descriptive statistics are methods for organizing and summarizing data. For example, tables or graphs are used to organize data, and descriptive values such as the average score are used to summarize data. A descriptive value for a population is called a parameter and a descriptive value for a sample is called a statistic .

6. Inferential Statistics Inferential statistics are methods for using sample data to make general conclusions (inferences) about populations. Because a sample is typically only a part of the whole population, sample data provide only limited information about the population. As a result, sample statistics are generally imperfect representatives of the corresponding population parameters.

7. Data Gathering and Organizing Data Representing Data Using Graphs and Charts Interpret Data

8. Data The measurements obtained in a research study are called the data . The goal of statistics is to help researchers organize and interpret the data.

9. Test yourself: Identify the data whether it is grouped or ungrouped. A. My friends in biology get a grade of 92, 84, 65, 76, 88, and 90. B. Allan 2 nd semester’s grade Course Name Course Grade No. of Units Biology 87 5 Statistics 90 3 Psychology 88 3

10. Two Types of Data Quantitative Data -deals with numbers and things you can measure objectively: such as height, width, and length. Temperature and humidity. Prices. Area and volume. Qualitative Data -deals with characteristics and descriptors that can’t be easily measured, but can be observed subjectively – such as smells, tastes, and textures.

11. Types of Quantitative Data Discrete data - is a count that can’t be made more precise - typically it involves integers - example: the number of children in your family Continuous data could be divided and reduced to finer and finer levels. example: height (precise scales – meters, centimeters, millimeters, and beyond)

12. Measures of Central Tendency Mean Median Mode

13. Mean The mean of numbers is the sum of the numbers divided by .  

15. Exercise: Solve for the mean: 4, 8, 1, 14, 9, 21, 12 46, 23, 92, 89, 77, 108 14, 27, 3, 82, 64, 34, 8, 51 21.3, 37.4, 11.6, 82.5, 17.2

16. Median The middle number or the mean of two middle numbers in a list of numbers that have been arranged in numerical order from smallest to largest or largest to smallest.

17. Example: A. 92, 84, 65, 76, 88 Arrange in numerical order (65, 76, 84, 88, 92) B. 245, 235, 220, 210 Arrange (210, 220, 235, 245) Get the mean of two middle numbers  

18. Exercise: Find the median: 4, 8, 1, 14, 9, 21, 12 46, 23, 92, 89, 77, 108 14, 27, 3, 82, 64, 34, 8, 51 21.3, 37.4, 11.6, 82.5, 17.2

19. Mode The mode is a list of numbers that occurs most frequently. Note: Some list of numbers do not have a mode. For instance, in the list 1, 6, 8, 10, 32, 15, 49, each number occurs exactly once.

20. Mode Note: Some list of numerical data can have more than one mode. For instance, in the list 4, 2, 2, 6, 2, 4, 7, 4 the number 2 occurs three times and so does number 4.

21. Exercise: Identify the mode: 4, 8, 1, 12, 9, 21, 12 18, 15, 21, 16, 15, 14, 15, 21 2, 5, 8, 9, 11, 4, 7, 23 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 8 12, 34, 12, 71, 48, 39, 71

22. REVIEW TO PROBABILITY

23. Experiment Experiment is a chance process that leads to a well-defined result called an outcome. For example: Flipping a coin Rolling a die

24. Outcome Outcome is the result of a single trail of an experiment. In flipping a coin the possible outcome is either a head or a tail. While in rolling a die the possible outcome is either 1 or 2 or 3 or 4 or 5 or 6. Experiment Outcome Flipping a coin Head (H) , Tail (T) Rolling a die 1, 2, 3, 4, 5, 6

25. Sample Space Sample space is the set of all the possible outcome or sample points. Experiment Sample space Flipping two coins HH, HT, TH, TT Rolling a die 1, 2, 3, 4, 5, 6

26. The number of students in a classroom. Answer: Discrete The weight of a bag of rice. Answer: Continuous The number of cars in a parking lot. Answer: Discrete The temperature of a cup of coffee. Answer: Continuous The number of pets in a household. Answer: Discrete The height of a basketball player. Answer: Continuous The number of pages in a book. Answer: Discrete The time taken to complete a race. Answer: Continuous The number of siblings a person has. Answer: Discrete The speed of a moving car. Answer: Continuous The amount of water in a glass, measured in milliliters. Answer: Continuous The number of books on a library shelf. Answer: Discrete The distance traveled by an airplane. Answer: Continuous The number of goals scored in a soccer match. Answer: Discrete The price of a product in dollars and cents. Answer: Continuous The number of chairs in a room. Answer: Discrete The amount of rainfall in a day, measured in millimeters. Answer: Continuous The number of steps a person takes in a day. Answer: Discrete The length of a piece of string, measured in centimeters. Answer: Continuous The number of employees in a company. Answer: Discrete The age of a tree, measured in years. Answer: Discrete The volume of a liquid in a container, measured in liters. Answer: Continuous The number of text messages sent in a day. Answer: Discrete The time spent watching a movie, measured in minutes. Answer: Continuous The number of apples in a basket. Answer: Discrete