Data Gathering Techniques

Essential Question:

What are the different methods for gathering data about a

population?

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.

Census

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

Sampling

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

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.

Sampling Methods

• Random• Self-Selected• Convenience• Systematic• Stratified• Cluster

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.

Self-Selected

• Also known as Voluntary Sample• Individuals volunteer to be part of the sample.

Convenience

• Individuals are selected based on how accessible they are.

Systematic

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

Stratified

• The individuals are organized into groups, and individuals from each group are selected

• Typically individuals are selected randomly from the groups.

Cluster

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

Reflect 1a

• Give an example of numerical data and an example of categorical data other than the examples we already spoke about.

Reflect 1b

• Asking your friends is an example of what type of sampling method? Explain

Reflect 1c

• Which sampling method do you think is most likely to result in a representative sample? Why?

Reflect 1d

• Which sampling method do you think would be least likely to result in a representative sample? Why?

Reflect 1e

• Explain why a researcher might use a sampling method rather than a census to gather information about a population.

Finding Statistics Using Various Sampling Methods

Salaries of all 30 employees are listed

Salaries at a Small company (in thousands of dollars)

21 24 26 28 30 32 33 35 37 41

44 46 47 49 50 51 52 54 55 57

58 62 62 64 64 65 70 71 73 80

Salaries of all 30 employees are listed

Salaries at a Small company (in thousands of dollars)

21 24 26 28 30 32 33 35 37 41

44 46 47 49 50 51 52 54 55 57

58 62 62 64 64 65 70 71 73 80

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.

Salaries of all 30 employees are listed

Salaries at a Small company (in thousands of dollars)

21 24 26 28 30 32 33 35 37 41

44 46 47 49 50 51 52 54 55 57

58 62 62 64 64 65 70 71 73 80

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

Salaries of all 30 employees are listed

Salaries at a Small company (in thousands of dollars)

21 24 26 28 30 32 33 35 37 41

44 46 47 49 50 51 52 54 55 57

58 62 62 64 64 65 70 71 73 80

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

Salaries of all 30 employees are listed

Salaries at a Small company (in thousands of dollars)

21 24 26 28 30 32 33 35 37 41

44 46 47 49 50 51 52 54 55 57

58 62 62 64 64 65 70 71 73 80

Take a random sample using a random number generator.Record the salaries, and then compute the sample’s

mean, rounding to the nearest whole number

Salaries of all 30 employees are listed

Salaries at a Small company (in thousands of dollars)

21 24 26 28 30 32 33 35 37 41

44 46 47 49 50 51 52 54 55 57

58 62 62 64 64 65 70 71 73 80

Compute the population’s mean, rounding to the nearest whole number

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?

Making Predictions from a Sample

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.

Use the proportions and the model below to predict the number of runners among

all adults living in the community.

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.

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?

Reflect

• What were the two numerical variables in the survey, and what were their possible values?

Reflect

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