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MATH 2200: Elementary Statistics

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LOOKING BACK

MODULE TWO SUMMARY

This module presented fundamentally and critically important measures that are essential for effectively describing, exploring, and comparing data.   Below is a summary of the key concepts with which you should be familiar

  • Quantitative Data
    • Grouped Frequency Distribution
    • Graphs
      • Stem & Leaf Plot
      • Histogram
        • Distribution
          • Skewed to the Left
          • Skewed to the Right
          • Symmetric
      • Boxplot
  • Descriptive Statistics ---calculate using technology and interpret
    • Measures of Center
      • Mean
        • Most important –uses all data values and used in other statistical calculations
      • Median
      • Mode
    • Measures of Variation
      • Range
      • Standard Deviation
        • Most important –uses all data values and used in other statistical calculations
      • Variance
    • Measures of Position
      • Percentiles
      • Quartiles
        • IQR—middle 50% of data set
        • Outliers—formula to determine if any exist
      • Standard z-scores

In the last sub-module, we shifted the focus to the basic concept and guidelines of probability, which is so important for the methods of inferential statistics introduced later in this course.   Furthermore, we discussed the most important type of probability distribution:  normal distributions, which will be used extensively in the following modules.

  • Probability
    • What is it?
    • Four guidelines
      • P(impossible event) = 0
      • P(certain event) = 1
      • All probabilities are between and include 0 and 1
        • Can be fractions, decimal, or percents
      • Sum of all probabilities is 1
  • Probability Distribution—what is it?
  • Normal Distribution
    • Characteristics
      • Continuous
      • Symmetric
      • Bell-shaped
      • Total “area” under the curve is 1 or 100%
    • Empirical Rule
      • About 68% of data values fall within one standard deviation of mean
      • About 95% of data values fall within two standard deviation of mean
      • About 99.7% of data values fall within three standard deviation of mean
  • Determine probability of an event (Type I) using calculator
    • Normalcdf (start value on left, end value on right, mean, std dev)
    • Four scenarios
      • Less Than
      • Greater Than
      • Between
      • Tails
  • Find the cutoff score for a given probability (Type II) using calculator
    • invNorm(area to LEFT of cutoff, mean, standard deviation)
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