Stats 1124: CH 2

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Stats 1124: CH 2
2012-01-17 02:33:37
Stats 1124

Chapter 2: Describing Distributions with Numbers
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  1. What is the mean?
    • The measures of the average!
    • Symbol: x(with line on top)
  2. What is the Median?
    Median(m): the value that has the middle position when n data points are put in order
  3. Compare Mean and Median in two ways
    1. If graph is mound and symmetric, mean and median are the same.

    2. If graph is skewed, mean moves away from the median toward the longer tail
  4. Why is median a resistant measure?
    Because it is NOT affected by an extreme observation(change).
  5. What are thw two measures of variablility?
    • 1. Range
    • 2. Standard Deviation
  6. What does the range give us?
    Range(R) = MAX - MIN , it gives us the spread of the entire data
  7. Why can the range be misleading? (2)
  8. What is standard Deviation?
    (s): It uses all the data points and describes the variation around the mean.

    It is a concept not a calculation!
  9. What is degrees of freedon? (df)
    Idea: The number of observations that are free to vary after the sample mean has been calculated
  10. What are the four properties of standard deviation?
  11. What is the five-number summary?
  12. What is interquartile range (IQR)?
    (Q3 - Q1): It gives us the spread of the middle 50% of the data
  13. What two values gives us the range?
    (Q1 - 1.5 x IQR) and (Q3 + 1.5 x IQR)
  14. What are suspected outliers?
    Any values that fall outside this range (Q1 - 1.5 x IQR) and (Q3 + 1.5 x IQR)
  15. How are boxplots best used?
    They are best used by a side-by-side comparison
  16. Why are Histograms only in 5 to 10 intervals?
    Bceause too many points(50) or too little (2) will cause the shape to look unappealing.

    • 50 points = not summarized enough
    • 2 points = too summarized
  17. What are three things about a Histogram thats different?
    • 1. large dataset
    • 2. left inclusion
    • 3. no overlap
  18. What are 4 things to look for when looking at the graph?
    • 1. Centre:(Midpoint)
    • 2. Spread:(Range)
    • 3. Outlier: (unusual points)
    • 4. Shape:( Symmetrical, skewed right and left)
  19. How can mean by increased and decreased?
    Mean can be increased by adding more data points and decreased by removing datapoints
  20. How to check if something is resistant or not?
    • Check if it affects the outliers.
    • Mean is sensitive to the influence of extreme observations(Changes a lot when something is added or deleted), therefore, NOT RESISTANT.

    If something is resistant to something then it DOESN'T change a lot, if it is NOT resistant to something then it CHANGES easily.
  21. Is range a resistant outlier?
    Range is NOT a resistant outlier.
  22. Is Median resistant or not?
    Median IS resistant