Frequency Distributions

Discussion

• It is very difacult to get meaning out of a bunch of raw data.
• A frequency distribution allows us to investigate the data.
  • We need to know the lowest and highest values of the data.
  • We then break the data into a number of classes
    • Each class should be the same width
    • Classes should not overlap
    • Each piece of data should belong to a single class.
  • We then count how many data items appear in each class.
  Example 1, number 10, page 766 (sort of)

  The data ranges from 20 to 34.  
  Let us divide into classes with width of 5
  The classes would be
     20-24, 25-29, 30-34
  
  20-24   12
  25-29   13
  30-34    7
  
      

  • The width of each class is 5 since each class contains 5 possible values.
  • 20, 25, and 30 are the lower class limits
  • 24, 29 and 34 are the upper class limits
  • 25-29 is the modal class since it contains the gratest number of values.
  • The midpoint of a class or the class mark is found by

         upper class limit + lower class limit
    M = -------------------------------------
                           2
        

  • So for the 20-24 class, the midpoint is (24+20)/2 = 22
  • Note, We can draw A picture of the frequency distribution called a histogram
    • Use the midpoint of the class for the x axis label
    • The x axis does not need to start at 0
    • The y axis must start at 0, but can be broken, but remember the previous section.
    • Make sure you label the axises.
  • A Frequency Polygon is the same, but a single line is used in place of polygons.

  Do Also

  Number 18, page 776 Use the data in 25, page 777

  Homework

  Page 765: 7, 9, 11, 15, 19, 25 Page 774: 13, 15, 17, 19