Sections 1'1 and 1'2

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Sections 1.1 and 1.2

• Displaying and Describing Data

2

• Categorical variables (qualitative)-
• Quantitative variables (numerical)-
• See book for working with categorical data. We
  will focus on quantitative data in lecture.
•  

   
3
Picturing Quantitative Variables

• Stemplot of Heights
• Split Stems
• Line up leaves

4
Picturing Quantitative Variables

• Histogram of Heights
• All classes should have same width
• Choosing class widths
• Data on a boundary.
• Height can be count or percentages

5
Describing shape.

• Symmetric.
• Skewed to left or right

Think Skewed to the tail.
6
Describing center.

• What is the typical height?
• What is the typical amount of pocket money?
• Two notions of center.
• Median 
• Mean

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Comparing Notions of Center

• For symmetric distributions (like height)
• For skewed distributions (like pocket money)
• For distributions with outliers.

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Which of the following is likely to have a mean
that is smaller than the median? a)      The
salaries of all National Football League players.
b)     The scores of students (out of 100
points) on a very easy exam in which most get
nearly perfect scores but a few do very poorly.
c)      The prices of homes in a large city.
d)     The scores of students (out of 100
points) on a very difficult exam in which most
get poor scores but a few do very well.
9
Describing spread.

• What is the spread of hours slept?
• What is the spread of pocket money?
• Two notions of spread.
• Five number summary / Boxplot  
• Single number summarizing spread standard
  deviation (s).

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Five number summary/Boxplot

• Example (hrs slept)
• Side by side boxplots useful for comparing.

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Standard deviation (s)
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• Suppose I gave 20 to every student as they
  walked into class? How would each of the
  following numbers change?
• The median of pocket money.
•  
• The mean of pocket money.
• The standard deviation of pocket money.

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Summary

• Categorical Variables
• Quantitative Variables
• Histograms and/or Stemplots
• Describe Shape, Center, and Spread
• Shape is often symmetric or skewed.
• Use mean or median for center.
• Use standard deviation or 5 number summary for
  spread.