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Statistics: Sampling, Frequency Distributions, and Graphs, Study notes of Mathematics

University of Nevada - Las Vegas (UNLV)Mathematics

An introduction to statistics, including definitions of data, statistics, population, sample, random sample, frequency distribution, and frequency. It also includes examples and exercises on constructing frequency distributions and histograms. The document emphasizes the importance of unbiased sampling and avoiding bias when selecting a sample.

Typology: Study notes

Pre 2010

Uploaded on 02/24/2010

koofers-user-798
koofers-user-798 🇺🇸

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Chapter 12. Section 1
Page 1
Section 12.1 – Sampling, Frequency Distributions, and Graphs
Homework (pg 605) problems 1-19
• Definition: Numerical information organized or listed is called data
• Definition: Statistics is a way of collecting, organizing, analyzing and interpreting data, as well as
drawing conclusions based on the data
• Definition: A population is the set containing all that is to be described and analyzed. A sample is
a subset of the population. Special care must be taken when choosing the sample, as it cannot be
biased in any way.
• Example: If you want to find out if individuals are against drinking alcohol, you wouldn’t ask only
those citizens in a bar.
• Example (Checkpoint 1): A city government wants to conduct a survey among the city’s homeless
to discover their opinions about required residence in city shelters from midnight until 6am.
a) Describe the population
b) A commissioner suggests obtaining a sample by surveying all the homeless people at the city’s
largest shelter. Is this a good idea?
Solution:a) The population is the city’s homeless
b) No, because those in a shelter are biased for them
Definition: A random sample is a sample obtained in such a way that every element in the population
has an equal chance of being selected for the sample.
• Example (Checkpoint 2): Why is Checkpoint 1b a bad way to sample, and how can one accomplish
this?
Solution: It is a bad sample because those that are not in a particular shelter on a particular night
have no chance of being selected. Getting a random sample of homeless would be difficult to
implement at best. But, if you could, round them all up, assign them a number and draw the
numbers like a lottery. Then they would all have an equal chance.
• Definition: A piece of data is called a data item, and the value it takes is called a data value.
• Definition: Frequency refers to the number of times a particular data value occurs. A frequency
distribution organizes the data in terms of the frequency (it lists all items with their corresponding
frequency).
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Chapter 12. Section 1 Page 1

Section 12.1 – Sampling, Frequency Distributions, and Graphs

Homework (pg 605) problems 1-

  • Definition : Numerical information organized or listed is called data
  • Definition : Statistics is a way of collecting, organizing, analyzing and interpreting data, as well as drawing conclusions based on the data
  • Definition : A population is the set containing all that is to be described and analyzed. A sample is a subset of the population. Special care must be taken when choosing the sample, as it cannot be biased in any way.
  • Example : If you want to find out if individuals are against drinking alcohol, you wouldn’t ask only those citizens in a bar.
  • Example (Checkpoint 1) : A city government wants to conduct a survey among the city’s homeless to discover their opinions about required residence in city shelters from midnight until 6am. a) Describe the population b) A commissioner suggests obtaining a sample by surveying all the homeless people at the city’s largest shelter. Is this a good idea? Solution : a) The population is the city’s homeless b) No, because those in a shelter are biased for them

Definition : A random sample is a sample obtained in such a way that every element in the population has an equal chance of being selected for the sample.

  • Example (Checkpoint 2) : Why is Checkpoint 1b a bad way to sample, and how can one accomplish this? Solution : It is a bad sample because those that are not in a particular shelter on a particular night have no chance of being selected. Getting a random sample of homeless would be difficult to implement at best. But, if you could, round them all up, assign them a number and draw the numbers like a lottery. Then they would all have an equal chance.
  • Definition : A piece of data is called a data item , and the value it takes is called a data value.
  • Definition : Frequency refers to the number of times a particular data value occurs. A frequency distribution organizes the data in terms of the frequency (it lists all items with their corresponding frequency).

Chapter 12. Section 1 Page 2

  • Example (Checkpoint 3) : Construct a frequency distribution for the grades in precalc below F, A, B, B, C, C, B, C A, A, C, C, D, C, B, D ,C, C, B, C Solution : Grade Frequency A 3 B 5 C 9 D 2 F 1 30 total
  • Definition : Data can be arranged into groups called classes , and then needs to be organized in a grouped frequency distribution.
  • Example (Checkpoint 4) : For the data below, use the classes 40-49, 50-59, 60-69, 70-79, 80-89 and 90-99 and construct a grouped frequency distribution for the following exam scores 73 58 68 75 94 79 96 79 87 83 89 52 99 97 89 58 95 77 75 81 75 73 73 62 69 76 77 71 50 57 41 98 77 71 69 90 75 Solution : Tally by going through list (1 indicates a tick mark) Class Tally Frequency 40-49 1 1 50-59 11111 5 60-69 1111 4 70-79 111111111111111 15 80-89 11111 5 90-99 1111111 7 / 37 total
  • Definition : A histogram is a bar graph with data values (or classes) and their corresponding frequencies. A frequency polygon is made from a histogram by connecting the middle of the bar with a line (we will not spend class time doing these examples, as they are not commonly used compared to the histogram).
  • Example : Construct a frequency histogram for Checkpoint 4

Solution :

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40-49 50-59 60-69 70-79 80-89 90- Test Scores

Frequency