Thinking Mathematically by Robert Blitzer

							  Thinking
Mathematically
                  Statistics:
 12.1 Sampling, Frequency Distributions, and Graphs
                 Statistics
Statistics is the science of data. This involves
  collecting, organizing, analyzing, and
  interpreting numerical information, as well
  as drawing conclusions based on the data.
               Types of Statistics
• Descriptive Statistics utilizes   • Inferential Statistics utilizes
  numerical and graphical             sample data to make
  methods to look for patterns        estimates, decisions,
  in a data set, to summarize         predictions, or other
  the information revealed in a       generalizations about a
  data set, and to present that       larger set of data.
  information in a convenient
  form.
      Populations and Samples
• A population is the set containing all the objects
  whose properties are to be analyzed
• A sample is a subset of the population.
• 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.
   Exercise Set 12.1 #1 (from text)
        Frequency Distribution
• Collected data presented in a two column table.
  The first column list the data values, the second
  column the number of times each value occurs.
   Exercise Set 12.1 #7
      A random sample of 30 college students is selected. Each
        student is asked how much time s/he spent on homework
        during the previous week. The following times are obtained:
          16, 24, 18, 21, 18, 16, 18, 17, 15, 21, 19, 17,
            17, 16, 19, 18, 15, 15, 20, 17, 15, 17, 24, 19,
            16, 20, 16, 19, 18, 17.
      Construct a frequency distribution for the data.
   Grouped Frequency Distribution
• Data is organized in to groups or classes.
• The minimum value for a class if the lower class
  limit, the maximum is the upper class limit.
• The difference between the lower class limit and
  the upper class limit is the class width and is the
  same for all classes.
• The grouped frequency distribution lists the
  number of data points in each class.
   Exercise Set 12.1 #17
      Construct a grouped frequency distribution for the age at which U.S.
        presidents were inaugurated (see text)
Histograms and Frequency Polygon
• In a histogram the vertical axis gives the
  frequency (or proportion) for each class of data
  (the horizontal axis).
• Like the histogram, the axis of a frequency
  polygon represent data class (horizontal) and
  frequency for that class (vertical). In the
  frequency polygon this data points are connected
  by line segments.
   Construct a histogram and a frequency polygon for the
     data in exercise 17.
        Stem-and-Leaf Display
• Data is ordered and grouped
   – Grouping is often by highest digit
• Left column is the ‘group number’
• Individual of the group are listed in right column
Construct a stem and leaf plot for the data in
  exercise 17.
  Thinking
Mathematically
                  Statistics:
 12.1 Sampling, Frequency Distributions, and Graphs