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This module introduces the concept of statistical sampling. Students are taught the difference between a simple random sample, stratified sample, cluster sample, systematic sample, and convenience sample. Example problems are provided, including an optional classroom activity.

Gathering information about an entire population often costs too much or is virtually impossible. Instead, we use a sample of the population. A sample should have the same characteristics as the population it is representing. Most statisticians use various methods of random sampling in an attempt to achieve this goal. This section will describe a few of the most common methods.

There are several different methods of random sampling . In each form of random sampling, each member of a population initially has an equal chance of being selected for the sample. Each method has pros and cons. The easiest method to describe is called a simple random sample . Any group of n individuals is equally likely to be chosen by any other group of n individuals if the simple random sampling technique is used. In other words, each sample of the same size has an equal chance of being selected. For example, suppose Lisa wants to form a four-person study group (herself and three other people) from her pre-calculus class, which has 31 members not including Lisa. To choose a simple random sample of size 3 from the other members of her class, Lisa could put all 31 names in a hat, shake the hat, close her eyes, and pick out 3 names. A more technological way is for Lisa to first list the last names of the members of her class together with a two-digit number as shown below.

Class roster
ID Name
00 Anselmo
01 Bautista
02 Bayani
03 Cheng
04 Cuarismo
05 Cuningham
06 Fontecha
07 Hong
08 Hoobler
09 Jiao
10 Khan
11 King
12 Legeny
13 Lundquist
14 Macierz
15 Motogawa
16 Okimoto
17 Patel
18 Price
19 Quizon
20 Reyes
21 Roquero
22 Roth
23 Rowell
24 Salangsang
25 Slade
26 Stracher
27 Tallai
28 Tran
29 Wai
30 Wood

Lisa can either use a table of random numbers (found in many statistics books as well as mathematical handbooks) or a calculator or computer to generate random numbers. For this example, suppose Lisa chooses to generate random numbers from a calculator. The numbers generated are:

  • .94360
  • .99832
  • .14669
  • .51470
  • .40581
  • .73381
  • .04399

Lisa reads two-digit groups until she has chosen three class members (that is, she reads .94360 as the groups 94, 43, 36, 60). Each random number may only contribute one class member. If she needed to, Lisa could have generated more random numbers.

The random numbers .94360 and .99832 do not contain appropriate two digit numbers. However the third random number, .14669, contains 14 (the fourth random number also contains 14), the fifth random number contains 05, and the seventh random number contains 04. The two-digit number 14 corresponds to Macierz, 05 corresponds to Cunningham, and 04 corresponds to Cuarismo. Besides herself, Lisa's group will consist of Marcierz, and Cunningham, and Cuarismo.

Besides simple random sampling, there are other forms of sampling that involve a chance process for getting the sample. Other well-known random sampling methods are the stratified sample, the cluster sample, and the systematic sample.

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Source:  OpenStax, Engr 2113 ece math. OpenStax CNX. Aug 27, 2010 Download for free at http://cnx.org/content/col11224/1.1
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