13.4 and 13.5

• The word average represents a number in the middle of a set of data.
• Just exactly what that is is ambiguous.
• We will look at four ways to measure the average of a dataset.
• The mean, or better yet the algebraic mean is the standard definition of average
  • x-bar for sample
  • μ for population.
  • x = Σx/n
• The median is the middle data.
  • Place the data in order.
  • If n is odd, it is the middle data item.
  • If n is even, it is the mean of the middle two numbers.
• The mode is the data item (or items) which occur most frequently
  • If all data items occur once, the set has no mode.
  • If more than one item occurs with the same multiplicity it is bimodal
  • This will vary depending on the book used.
• The midrange is (high+low)/2
• Measurements of position.
  • Percentile is your ranking in the population.
    • If you are in the n^th percentile, you scored better than n% of the population, and less well than (100-n)%.
  • Quartile scores are also a measurement of position.
    • Order the data
    • Find the median of the data. This is Q₂
    • Find the median of the lower half of the data, not including Q₂, this is Q₁
    • Find the median of the upper half of the data, not including Q₂, this is Q₃
• Measures of dispersion
  • Range = high-low
  • Standard deviation
    • s for a sample
    • σ for a population.
    • s = sqrt(Σ(x-x_bar)²/(n-1))