3-6 6 th grade math Sampling Methods

Objective To understand how the method of sampling determines how representative the sample is of the population. Why? To understand that the sample selected to study must represent the population being investigated if inferences about the population are to be valid. The best way to choose a sample is randomly. A random sample is usually a good representation of the population you are drawing from. But contacting all members of the sample might not be possible. Many methods of gathering data have some bias. Paper surveys may not reflect those who are too busy to reply or who have no interest in the topic of the survey.

California State Standards SDP 2.2 : Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population. SDP 2.4 : Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

Vocabulary Random Sampling – A sampling method in which each person or thing has an equal chance of being chosen Asking people off the street Representative – A random sampling which is a good match for the population Asking people at a doctor’s office about taking medicines, in general (RR) = Random and Representative!!

More Vocabulary… Biased – A sample which does not mirror the population Asking people at a doctor’s office about taking a specific medicine, especially if the type of medicine ≈ the type of doctor Convenience Sampling – A sampling method where any convenient method is used to choose the sample Asking people at a doctor’s office about taking a specific medicine, especially if the type of medicine ≈ the type of doctor Responses to a Survey – A form to fill out (asking sampling questions) is usually biased Fill out a form-survey about your car buying experience (BCRS) = Bias is Convenient and Responding to a Survey

How to Work with Sampling Methods 1) Randomly choose an ‘X’ number samples. 2) Find mean, median, mode. Are they similar, statistically? 3) Identify the sample being used, and does it represent the population being studied? Was there bias? 1)Choose any , 53, 127, 176, 180, 284, 304, 311, 426, 608 2) Mean = 2329/10 = ≈ 233 Median = = 464/2 = 232 Mode = none Yes statistically similar. 3) Sample = Number of districts in states Not bias because it was random. (RR)

How to Work with Sampling Methods 1) Randomly choose an ‘X’ number samples. 2) Find mean, median, mode. Are they similar, statistically? 3) Identify the sample being used, and does it represent the population being studied? Was there bias? 1)Choose top , 180, 501, 608, 661, 674, 705, 929, 994, ) Mean = 6361/10 = ≈ 636 Median = = 1335/2 = ≈ 668 Mode = none Not statistically similar. 3) Sample = Number of districts in states Yes, biased because it was conveniently chosen. (BCRS)

How to Work with Sampling Methods 1 ) Randomly choose an ‘X’ number samples. 2) Find mean, median, mode. Are they similar, statistically? 3) Identify the sample being used, and does it represent the population being studied? Was there bias? 1) 10 people responded to a written survey: pairs of shoes. 1, 3, 5, 5, 6, 6, 6, 7, 8, 12 2) Mean = 59/10 = 5.9 ≈ 6 Median = 6 Mode = 6 Yes, statistically similar. 3) Sample = pairs of shoes Yes, biased because it was conveniently chosen. (BCRS)

Try It! A. Tell whether each sample is representative (RR) or biased (BCRS). B. Identify if: random sampling, convenience sampling, or responses to a survey. 1)Mailing questionnaire to all eligible voters. 12% respond and return the form. 2)Principal questions every student whose locker number ends in a 9 to gather student input about plans for a new library. 1)A. Biased B. Responses to a survey (BCRS) 2) A. Representative B. Random sampling (RR)

Objective Review To understand how the method of sampling determines how representative the sample is of the population. Why? You now understand that the sample selected to study must represent the population being investigated if inferences about the population are to be valid. You know that the best way to choose a sample is randomly. A random sample is usually a good representation of the population you are drawing from. Understand that contacting all members of the sample might not be possible. You also know that many methods of gathering data have some bias. Paper surveys may not reflect those who are too busy to reply or who have no interest in the topic of the survey.

Independent Practice Complete problems 3-5 You may work with a partner to discuss the answers. For extra points, write the reasons for your answers. If time, complete Mixed Review: 6-9 If still more time, work on Accelerated Math.