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Section 1

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Intro to Statistics

Intro to Statistics

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Transcript

  • 1. CHAPTER 1 Exploring Data
  • 2. Displaying Distributions with Graphs What Graphs to Use When
  • 3. VOCABULARY
    • Individuals – objects described by a set of data. They may be people, but they may be animals or things.
    • Variable – any characteristic of an individual.
  • 4. TYPES OF VARIABLES
    • Categorical – groups or categories an individual belongs to (job title, gender, etc.)
    • Quantitative – numerical values for which it makes sense to do arithmetic operations on (height, weight, income, etc.)
  • 5. WAYS TO DISPLAY DATA
    • Dotplot
    • Histogram
    • Bar Chart
    • Stemplot
    • Timeplot
    • Boxplot and Modified Boxplot
    • Let’s look at the first three.
  • 6. DOTPLOT
    • Drawing a horizontal line to represent the variable
    • Make a number scale for the values of the variable.
    • Mark a dot at the appropriate place for each observation
  • 7. HISTOGRAM
    • Used when variables take many values
    • Group values of the variables together
    • Most common graph used with one quantitative variable
  • 8. BAR CHART
    • Used when data is categorical
    • Not used until later in Statistics course
  • 9. INTERPRETING DISTRIBUTIONS Learning How to CUSS
  • 10. CUSS
    • C – give the center of the distribution (value that divides the observations so that half are above and half are below)
    • U – give any unusual features of the distribution (outlier, gap, multiple peaks)
    • S – give the spread of the graph (use range = largest value – smallest value)
    • S – give the shape of the graph
  • 11. CUSS Continued
    • Outlier – an individual observation that falls outside the overall pattern of the graph. (unusual feature)
    • Possible shapes
      • Symmetric – if the right and left sides are approximately mirror images of each other
      • Skewed to the right – the right side of the distribution extends out further to the right
      • Skewed to the left – the left side of the distribution extends out further to the left
  • 12. EXAMPLE
    • Center –
    • Unusual Features –
    • Spread –
    • Shape –
  • 13. EXAMPLE
    • Center – the center is approx. 13%
    • Unusual Features – there are possible outliers and two gaps
    • Spread – the range is approx. 16
    • Shape – close to symmetric without outliers
  • 14. ASSIGNMENT
    • Page 8-9 #1.1 - 1.3
    • Page 15-18 #1.4 – 1.8
    • CUSS Worksheet
  • 15. STEMPLOTS
    • Used with small data sets
    • Made by separating each observation into a stem , consisting of all but the rightmost digit, and a leaf , the final digit.
    • Preserves the actual value of each observation.
    3 | 4, 6 4 | 3 5 | 2, 4, 5, 7, 8 6 | 0, 0, 1, 2, 4, 4, 4, 5, 6, 9 7 | 0, 1, 3, 4, 6, 7, 8, 8 8 | 1, 1, 2, 3, 3, 6, 7, 8, 9, 9 9 | 7
  • 16. VARIATION OF A STEMPLOT
    • Called split stems
    • Each stem appears twice
    • Leaves 0 to 4 go on the upper stem
    • Leaves 5 to 9 go on the lower stem
    1 | 0,1,1,3 1 | 8, 9, 9, 9, 9, 9 2 | 0, 0, 1,2,2,4 2 | 5,7,7,9 3 | 0, 1 3 | 5,5,6
  • 17. TIMEPLOT
    • Plots each observation against the time at which it was measured
    • Time scale is the horizontal axis
    • Variable of interest is the vertical axis
    • Look for trends, or overall patterns
  • 18. ASSIGNMENT
    • Page 18-22 #1.9 – 1.13
    • Page 24-28 #1.16, 1.17, 1.20, 1.21
    • Smokers vs. Ex-Smokers Worksheet
    • Prepare for Quiz 1.1

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