1. Data Gathering Techniques

2. Essential Question: What are the different methods for gathering data about a population?

3. Statistics Works with data. Data could be numerical or categorical. Collect data about a population by surveying some or all of the individuals in the population.

4. Census When all the individuals in a population are surveyed or studied.

5. Sampling When only some of the individuals in a population are surveyed or studied.

6. Statistic A number that summarizes a characteristic of a sample. Can be used to estimate parameters Samples that result in accurate estimates are said to be representative of the population.

7. Sampling Methods Random Self-Selected Convenience Systematic Stratified Cluster

8. Random Each individual in the population has an equal chance of being selected Individuals are assigned a number and then a random number generator is used to select the sample.

9. Self-Selected Also known as Voluntary Sample Individuals volunteer to be part of the sample.

10. Convenience Individuals are selected based on how accessible they are.

11. Systematic Members of the sample are chosen according to a rule, such as every nth individual in the population.

12. Stratified The individuals are organized into groups, and individuals from each group are selected Typically individuals are selected randomly from the groups.

13. Cluster Individuals are organized into groups, and all the individuals in just some of the groups are selected.

14. Reflect 1a Give an example of numerical data and an example of categorical data other than the examples we already spoke about.

15. Reflect 1b Asking your friends is an example of what type of sampling method? Explain

16. Reflect 1c Which sampling method do you think is most likely to result in a representative sample? Why?

17. Reflect 1d Which sampling method do you think would be least likely to result in a representative sample? Why?

18. Reflect 1e Explain why a researcher might use a sampling method rather than a census to gather information about a population.

19. Finding Statistics Using Various Sampling Methods

20. Salaries of all 30 employees are listed Salaries at a Small company (in thousands of dollars) 21242628303233353741 44464749505152545557 5862 64 6570717380

21. Salaries of all 30 employees are listed Salaries at a Small company (in thousands of dollars) 21242628303233353741 44464749505152545557 5862 64 6570717380 Suppose individuals whose salaries are 51, 57, 58, 65, 70 and 73 volunteer to be in the sample. Compute the self-selected sample’s mean, rounding to the nearest whole number.

22. Salaries of all 30 employees are listed Salaries at a Small company (in thousands of dollars) 21242628303233353741 44464749505152545557 5862 64 6570717380 Take a convenience sample by choosing the 6 numbers in the first two columns of the table. Record the salaries, and then compute the sample’s mean, rounding to the nearest whole number

23. Salaries of all 30 employees are listed Salaries at a Small company (in thousands of dollars) 21242628303233353741 44464749505152545557 5862 64 6570717380 Take a systematic sample by choosing every fifth number in the list, reading from left to right in each row. Record the salaries, and then compute the sample’s mean, rounding to the nearest whole number

24. Salaries of all 30 employees are listed Salaries at a Small company (in thousands of dollars) 21242628303233353741 44464749505152545557 5862 64 6570717380 Take a random sample using a random number generator. Record the salaries, and then compute the sample’s mean, rounding to the nearest whole numberrandom number generator

25. Salaries of all 30 employees are listed Salaries at a Small company (in thousands of dollars) 21242628303233353741 44464749505152545557 5862 64 6570717380 Compute the population’s mean, rounding to the nearest whole number

26. Reflect List the four samples from best to worst in terms of how well each sample mean estimates the population mean. How do the best and worst sampling methods from your list compare to your answers to Reflect Questions 1c and 1d?

27. Making Predictions from a Sample

29. Calculate the following proportions from the sample data: Proportion of adults who get regular cardio exercise Proportion of runners among those who get regular cardio exercise.

30. Use the proportions and the model below to predict the number of runners among all adults living in the community.

31. Calculate the following from the sample data: Mean duration of exercise for those who get regular cardio exercise. Mean frequency of exercise for those who get regular cardio exercise. Use these means to predict the number of hours spent exercising each week.

32. Reflect One of the categorical variables in the survey was regular cardio exercise. That variable had only two possible values: yes or no. What was the other categorical variable, and what are its possible values?

33. Reflect What were the two numerical variables in the survey, and what were their possible values?

34. Reflect How much confidence do you have in the predictions made from the results of the survey? Explain your reasoning.