Graphs of samples to graphs of populations

• Histograms to density curves (quantitative variables) (From "choppy" to "smooth.")
  
  • To do this, we have to consider the sample size increasing and increasing.
  • In the histogram of the sample, make the width of the bins narrower and narrower until you can barely see the vertical bars as separate. (You need a large-enough sample that you still have many scores in each of the bins along the horizontal axis.)
  • Continue to make the width of each of the bins even narrower and you can no longer see the vertical bars as separate. That gives you a smooth density curve.
    
    
• Bar graphs of the sample to bar graphs of the population (categorical variables) (There is very little difference between these!)
  • When we make a bar graph of a sample, we can make the vertical axis scale either the counts (frequencies) or the percentages/proportions.
  • The bar graph of a population is always given with the vertical axis scale as the percentages/proportions.

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