Sampling, Frequency Distribution, and Graphs

• Statistics is a mathematical science pertaining to the collection, interpretation and presentation of data.
• attributed to Benjamin Disraeli and popularized in the U.S. by Mark Twain: There are three kinds of lies: lies, damned lies, and statistics. - Wikipedia.
• Data, the numbers that we collect
• How we collect, and analyze this data is statistics.
• Descriptive Statistics is concerned with collecting, organizing, summarizing, and presenting the data.
• Inferential Statistics is involved with making generalizations and reaching conclusions about the data.
• We are generally concerned with a population or the set from which we are collecting data.
• When the population is too large, we sample the population, or collect information about a sub-group 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.
  • Is asking you (this class) questions a random sample of the student body?
  • How about asking those working out in McComb field house?
  • How about asking those walking across campus?
  • How about mailing an questioner to everyone on campus?
  • How about ...
  • This is a basic problem with statistics.
• If the sample exhibits characteristics typical of the sampled population, the sample is called representative
• Do number 2, page 641
• A frequency distribution is constructed by
  • Selecting a class width
  • Forming classes of this width from the lower limit to the upper limit
  • Counting the number of data items that occur in each class.
• Example: Build a frequency distribution for the following data:

  22, 24, 21, 19, 24, 25, 28, 18, 13, 29, 22, 25
  
      Use a lower limit of 10, and a class width of 4.
  
      Classes : 10 - 14,  15 - 19,  20 - 24,  25 - 29
      Count the data in each class
      10-14  1      1
      15-19  11     2
      20-24  11111  5
      25-29  1111   4
      n = 12
      

• Do number 10, page 641
• Each class, has an upper class limit and a lower class limit.
• A Histogram is constructed by
  • Label the X axis with the classes from your frequency distribution
  • Label the Y axis with values corresponding to the frequencies from the frequency distribution.
  • Draw a rectangle at each value.
  • 
• A frequency polygon is constructed the same way, but a single line, in place of the boxes, is used.
• 
• A stem and leaf plot is constructed by
  • Selecting the first few digits of the data as the stem
  • Recording the last digit as the leaf.

    
    	 1| 9 8 3
    	 2| 2 4 1 4 5 8 9 2 5
    	 
    	 

• Do number 28, page 643
• Do number 32 page 644

Homework