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Mastering Elementary Applied Statistics: Interpret Data with Precision

Discover the essence of statistics, from collecting to interpreting numerical facts, through real-life examples and practical techniques. Learn about representative samples, categorical and quantitative variables, distributions, and displaying data with graphs.

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Mastering Elementary Applied Statistics: Interpret Data with Precision

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  1. Elementary Applied Statistics Kathy Ensor, Chair Department of Statistics

  2. What is Statistics? • “Statistics is the science of collecting, organizing, and interpreting numerical facts, which we call data”. Pg xxv • Based on a “representative sample” what can we say about the population of interest? • Use of statistics is pervasive in our society. • Examples?

  3. Data? • Numerical facts? • Numerical summaries of what? • Sampling unit - the object or individual on which we are taking a measurement • Sampling frame or population - the group from which the sampling units are selected • Variable - the characteristic of the sampling unit that we measure

  4. Categorical Variable • The sampling unit belongs to one of several groups. • Examples? - time for you to speak up! • Nominal - No ordering to the categories (blue, red, green, yellow) • Ordinal - there is a natural ordering to the categories (excellent, very good, good, …)

  5. Quantitative variable • Numerical measures of a variable • Examples? • Arithmetic operations make sense (adding, dividing…) • Ratio and interval scales

  6. Distribution • A variable can take on a range of values. • The values do not occur in equal numbers • “The distribution of a variable tells us what values it takes and how often it takes these values.” • Variables exhibit variation; the distribution is the pattern of this variation

  7. Displaying Distributions with Graphs • Categorical data • Pie charts • Bar charts • A plot of the count for each category of the variable. • What information can you glean from these graphs? Which is the better of the two?

  8. Quantitative Variables • Stemplots (stem and leaf plot) • Back to back stem and leaf plot • describing two variables. • Histogram • frequency or relative frequency of the number of values of the variable falling into the specified interval.

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