Chapter 3, part C - Hanover College

Chapter 3, part C - Hanover College

Chapter 3, part C III. Uses of means and standard deviations Of course we dont just calculate measures of location and dispersion just because we can, they have very important uses. A. Z-scores A z-score measures the relative location of an item

in the data set. It also measures the number of standard deviations an observation lies from the mean. xi x zi s

For example, the airline price of $175 has a z-score=(175-219)/45.47 = -.97. This means that a price of $175 falls almost one standard deviation below the mean. B. Chebyshevs Theorem Chebyshevs: At least (1-1/k2) of the items in a data set must be within k standard deviations from the

mean, where k is any value greater than 1. In other words, the theorem tells us the % of items that must be within a specified number of standard deviations from the mean. Implications If k=2, at least 75% of the data lie within s=2 of the mean. How? (1-1/4)=.75 or 75%. If k=3, this fraction rises to 89% of the data.

If k=4, this fraction rises to 94% of the data. Example: A microeconomics exam has a mean of 72 with a standard deviation of 4. What % of the class falls between 64 and 80 on their exam? Calculate the z-scores for both 64 and 80 to find k and then use Chebyshevs theorem to answer the question. C. The Empirical Rule If the data are distributed normally (bell-shaped), the

empirical rule tells us that: Approximately 68% of the data will be within s=1 of the mean. 95% of the data will be within s=2 of the mean. all of the data will be within s=3 of the mean. D. Detecting Outliers The empirical rule says that almost all observations will fall within s=3 of the mean.

Thus, if an observation has a z-score of greater than 3 (in absolute value), it may be considered an outlier. What to do about an outlier? If its a case of an erroneous value (i.e. a typo), try to correct it. If its valid data, arguments can be made (for and against) dropping it from the sample.

Recently Viewed Presentations

  • Learner Survey Results - compmat.wcape.school.za

    Learner Survey Results - compmat.wcape.school.za

    Three course meal or Buffet? Three course. Question 4. Theme? Masquerade Ball. Will the Matric Dance be held inside or Outside? Should there be an open bar to serve beverages? Should we have a three-course meal or buffet? What are...
  • Snímka 1 - truni.sk

    Snímka 1 - truni.sk

    citlivosť na nachádzanie principiálnych odpovedí nielen teoretických, ale aj praktických problémov silný záujem o štúdium literatúry, filozofických diel, ale aj beletrie či kníh z iných vedných disciplín odvaha argumentovať, samostatne zdôvodňovať svoje postoje a názory kritický intelekt
  • RHYTHM BASICS - Drama Queensland

    RHYTHM BASICS - Drama Queensland

    RHYTHM BASICS. NAMES, VISUAL CUES AND RHYTHM CHALLENGES! Ta (Crotchet) = 1 beat. Ti Ti(2 Quavers) = 1 beat (half a beat each) Sa (Crotchet rest) = 1 beat rest (no sound) ta. STAMP ONE FOOT. ta. CLAP YOUR HANDS...
  • Governance Development Alexis Rickus Community Academies Trust Teaching

    Governance Development Alexis Rickus Community Academies Trust Teaching

    Rainbow maths- I like it because it helps times tables really quickly (C) There are so many ideas presented in the Focus Groups - might be good to stress this is only a small sample and we will collate further....
  • Genetics Primer - Weebly

    Genetics Primer - Weebly

    These units are now known as genes- the basic units of heredity. Mendel's Work formed the foundation for later scientific achievements that heralded the era of modern genetics- the study of the function and behavior of genes. DNA.
  • TOGAF EA Capability Map - Sparx Systems

    TOGAF EA Capability Map - Sparx Systems

    TOGAF and ArchiMate at The Open Group. Eclipse Process Framework (EPF) at the Eclipse Foundation. Business partners with Sparx, HP, and IBM. NIEM History. National Information Exchange Model (NIEM) was initiated in 2005 by U.S. Department of Justice (DOJ) and...
  • SOME MEN SUCCEED BECAUSE THEY ARE DESTINED TO,

    SOME MEN SUCCEED BECAUSE THEY ARE DESTINED TO,

    Decreased oxygen delivery. Anaerobic metabolism. Decreased ATP production. Lactic acid formation. Failure of Na+/K+ pump *Accumulation of Na+ in cell. Cellular swelling AND organelle swelling
  • C

    C

    Different approaches for data anaalysise.g. t-test, SDI,Youden plots & Levey-Jennings plots. New quality initiatives. The six sigma process. Lean production. ISO 9000. The six sigma process. The six sigma control is an evolution in quality management .