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Pie charts: no missing data

The following pie charts have the “Other/Unknown” category included (since the percentages must add to 100%). The chart in [link] is organized by the size of each wedge, which makes it a more visually informative graph than the unsorted, alphabetical graph in [link] .

Sampling

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 three 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 three 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 in [link] :

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

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

  • 0.94360
  • 0.99832
  • 0.14669
  • 0.51470
  • 0.40581
  • 0.73381
  • 0.04399

Lisa reads two-digit groups until she has chosen three class members (that is, she reads 0.94360 as the groups 94, 43, 36, 60). Each random number may only contribute one class member. If she needed to, Lisacould have generated more random numbers.

The random numbers 0.94360 and 0.99832 do not contain appropriate two digit numbers. However the third random number, 0.14669, 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 Cuningham, and 04 corresponds to Cuarismo. Besides herself, Lisa’s group will consist of Marcierz, Cuningham, and Cuarismo.

To generate random numbers:

  • Press MATH.
  • Arrow over to PRB.
  • Press 5:randInt(. Enter 0, 30).
  • Press ENTER for the first random number.
  • Press ENTER two more times for the other 2 random numbers. If there is a repeat press ENTER again.

Note: randInt(0, 30, 3) will generate 3 random numbers.

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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