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Probability & Statistics

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Presentation on theme: "Probability & Statistics"— Presentation transcript:

1 Probability & Statistics
Sampling Techniques

2 Sampling Techniques 13.1 Sampling Techniques
T. Serino 13.1 Sampling Techniques Population: All items or people of interest. Sample: Some items of a population.

3 Sampling Techniques T. Serino Statisticians often use a sample in order to make predictions about a whole population. When a statistician draws a conclusion from a sample, there is always the possibility that the conclusion is incorrect.

4 Sampling Techniques Why use a sample instead of a population?
T. Serino Why use a sample instead of a population? 1.  It is often impossible to obtain data on an entire population. 2.  Sampling is less expensive because collecting data takes less time and effort. More simply put… Studying samples saves and Time , money Effort

5 Sampling Techniques T. Serino In this unit, we will study some sampling techniques that attempt to collect unbiased samples of different populations. An unbiased sample is a small replica of the entire population. Definition: Unbiased:  1. having no bias or prejudice; fair or impartial   statistics (of a sample) not affected by any extraneous factors, conflated variables, or selectivity which influence its distribution; random

6 Sampling Techniques T. Serino If care isn't taken while collecting data or selecting a sample of the population, results could be biased. Definition: Bias:  a particular tendency or inclination, especially one that prevents unprejudiced consideration of a question; prejudice.

7 Sampling Techniques Random Sampling
T. Serino Sampling Techniques Random Sampling A sample drawn so that each item in the population has an equal chance of being selected. For example, a jar contains 200 marbles that are identical except for color. Half of the marbles are red and the other half of the marbles are blue. A random sample can be easily achieved by selecting marbles from the jar (without looking).

8 Sampling Techniques Systematic Sampling
T. Serino Systematic Sampling A sample obtained by drawing every nth item on a list or production line. (The first item should be determined by using a random number.) For example, to determine how often damaged items are produced, every tenth item is checked for damage. (In this example, n = 10.)

9 Sampling Techniques Cluster Sampling (or Area Sample)
T. Serino Cluster Sampling (or Area Sample) A random selection of groups or units. (Groups are often geographic locations.) For example, to estimate the average income of the residents of Lynn, a random sample of 100 residents was taken from each zip code in the city.

10 Sampling Techniques Stratified Sampling
T. Serino Stratified Sampling Dividing the population by characteristics that can usually be ordered by level. (Income, career, and social status are typical stratified characteristics, but gender, race, or religion can also be considered stratified.) For example, upper income, middle income, and lower income families were sampled to determine the average number of children per household.

11 Sampling Techniques Convenience Sampling
T. Serino Convenience Sampling Data that is easily or readily obtained. (Warning: This type of sampling can be extremely biased) For example, a teacher was interested in predicting who would become the senior prom queen. His period two class consisted of all seniors. He surveyed the period two class to see who they would vote for at the prom.

12 Sampling Techniques Review: 5 Sampling Techniques
T. Serino Review: 5 Sampling Techniques Random Sampling: Blindly choosing from a whole population Systematic Sampling: Choosing every nth item Cluster Sampling: Taking a sample from different Areas or groups Stratified Sampling: Taking samples from different levels Convenience Sampling: Sampling whatever is easy

13 Sampling Techniques Try this.
T. Serino Try this. Identify the sampling technique described. a. A raffle ticket is drawn by a blindfolded person at a festival to win a grand prize. b. Students at an elementary school are classified according to their present grade level. Then, a random sample of three students from each grade is chosen to represent their class. c. Every sixth car on highway is stopped for a vehicle inspection.

14 Sampling Techniques Try this.
T. Serino Try this. d. Voters are classified based on their polling location. A random sample of four polling locations is selected. All the voters from the precinct are included in the sample. e. The first 20 people entering a water park are asked if they are wearing sunscreen.

15 athematical M D ecision aking

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