Chapter Three -
Data Descriptions

  • Measures of Central Tendency

  • Measures of Variation

  • Measures of Position

  • Exploratory Data Analysis


    1. Definitions:

    Statistic  - A characteristic or measure obtained by using the data values from a sample (This is usually denoted by ROMAN letters)

    When I say "ROMAN" letters, I mean "A,B,C,D, etc."

    Parameter - A characteristic or measure obtained by using the data values from a population (This is usually denoted by GREEK letters)

    When I say "GREEK" letters, I mean (see below):

    2. THE GREEK ALPHABET (abbreviated)
    Greek Letter
    Upper and lower case
    Spoken as (in English): Special Meaning
    (in Math):
    Roman Letter equivalent:
    A,a "ALPHA" A,a
    W,w "OMEGA" ("O-MAY-GAH") O,o
    B,b "BETA" ("BAY-TAH") B,b
    G,g "GAMMA" G,g
    D,d "DELTA" Expresses a change in a quantity D,d
    E,e "EPSILON" E,e
    P,p "PI" Either "Multipication", or 
    the special number in geometry "3.1415~"
    S,s "SIGMA" Addition S,s
    Q,q "THETA" ("THAY-TAH") Geometric Angle Th (as in "the")

    These are just a few. There are
    These symbols may seem strange, but the SIGMA will be VERY important, as you will see soon.


    Measures of Central Tendency

    The basic idea here is that, in a given data set, we want to know where the "middle of the pack" is located. There are four different ways to do this. They are:

    Think of it this way: You know the expression "behind the power curve". How do we know if we are ahead , behind, or right on the "power curve"?  In order to know this, we need to have a good , numerical measurement of where the majority of our data points are located. It might be that the high score is a 100% on a test, and the lowest is a 60%.  But what if a majority of the students got at least a 70%, and no better than 75%? The mean, median, the mode, and the midrange help us figure out the boundaries of the "power curve".


     Read Chapter 3 in the textbook