Introduction

Context of example data

Fictional Extraction Example

Suppose a man, we'll call him Bob Prentice, from England; owns an oil company which operates 1000 deep water drilling rigs...

Bob wants to maximize his profits (barrels of oil extracted) while minimizing his expenditures (operating costs).

So Bob gathers data on how many barrels of oil each of his 1000 rigs extracted in 1 month because, Bob might want to shut down rigs which do not extract much oil, but still cause him to pay the substantial operating costs.

• The resulting data file is available at the following link:
  How will Bob describe his data?

  Descriptive Statistics

  Describing Data

  Bob is interested in describing the extraction and cost of his rigs. But, he does not want to look at all 1000 rigs' data (population) and instead decides to draw at random 10 rigs' data (sample) which is available on the next slide (Table 1).

  • After displaying his data (as covered in Module 2), with a variety of tables and figures (graphs), Bob will likely use Descriptive Statistics to describe his data.
  • Recall the goals of science and how we achieve them from Module 1:
    • Observation yields Description
    • Experimentation yields Explanation
    • Modeling yields Prediction
  • Descriptive Statistics only allow us to describe the
    data.

  Data: Extraction & Cost Sample (n = 10)

  Table 1: Raw Data for One Month

  rig	barrels	costs
  065	166	570
  142	185	560
  198	159	520
  277	207	580
  408	194	530
  533	191	560
  621	176	510
  788	216	550
  796	199	560
  915	228	560

  
  

  ``rig'' = identification number; ``barrels'' = 1,000 barrels extracted;
  ``costs'' = 1,000 USD

  Notation

  A note about Notation

  • Generally, variables are given capital letters, commonly X and Y.
  • Subscripts are used to identify each score on a variable.
    • A set of scores on Variable X
    • So that scores can be `called' = 35; = 22 ... = 77
  • Multiple subscripts can be used to identify a score located at a particular row (i) and column (j).
    • So, we can use the convention to identify a particular score, such as = 51
    • Which indicates that score 51 is located in the 2nd row and in the 3rd column of a table of data.

  Summation

  Use and rules of Sigma as Summation

  Please note that:

  • The is read as the sum of the values of X
    • Such as ...
    • Where n is the number of scores of variable X.
  • The is read as the sum of the squared values of X.
    • Such as ...
  • Which is very different from the following.
  • The is read as the square of the sum of the values of X
    • Such as
  
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