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Chapter 5 ~ Exploring Data:

Chapter 5 ~ Exploring Data:. Distributions. Recall:. individual ~ the objects described by a set of data. May be people or may also be animals or things. variable ~ any characteristic of an individual. A variable can take different values for different individuals.

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Chapter 5 ~ Exploring Data:

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  1. Chapter 5 ~ Exploring Data: Distributions

  2. Recall: • individual ~ the objects described by a set of data. May be people or may also be animals or things. • variable ~ any characteristic of an individual. A variable can take different values for different individuals. Exploratory Data Analysis: 1. Examine each variable by itself and then the relationship among them. 2. Begin with a graph or graphs, then add numerical summaries of specific aspects of the data.

  3. Displaying Distributions: Histograms (5.1) Distribution – The pattern of outcomes of a variable; it tells us what values the variable takes and how often it takes these values. • Histogram • The graph of the distribution of outcomes (often divided into classes) for a single variable. Figure 5.2: Histogram of the percent of Hispanics among the adult residents of the states (p. 183)

  4. EXAMPLE: Construct a histogram given the following data. How many pieces of data are there? • STEP 1: Choose the classes by dividing the range of data into classes of equal width (individuals fit into one class). (width of 3) • STEP 2: Count the individuals in each class (this is the height of the bar).(numbers in the count column above) • STEP 3: Draw the histogram: • The horizontal axis is marked off into equal class widths. • The vertical axis contains the scale of counts (frequency of occurrences) for each class. There are 3 + 2 + 5 + 4 + 2 = 16 pieces of data.

  5. Defining a class … • When constructing a histogram, each piece of data must fall into one class. • Each class must be of equal width. • For any given data set, there is more than one way to define the classes. • Either you are instructed as to how to define the classes, or you must determine the class based on some criteria.

  6. (do at your seats) EXAMPLE:Given the following 18 quiz scores (out of 30 points), construct a histogram. • Acceptable class widths? • Fill in a table with your decided class size. class count • Draw the histogram.

  7. Since there is one student that obtained a perfect score, it makes sense to have the last class end with 30. I. Class size of 3 Since there are no students that obtained scores in the first two classes, one may opt not to include these classes on the histogram. II. Class size of 5

  8. Interpreting Histograms (5.2) • Shape Regular Single-Peak Distributions: (tail trails to the right) (tail trails to the left) • Irregular Clustered Distributions: Two separate clusters, graphing two individuals (state and private schools) Figure 5.4 (p. 186)

  9. center ~ for now, we can think of the center of a distribution as the midpoint. • spread ~ is stating its smallest and largest values. • outliers ~ a piece or pieces of data that fall outside the overall pattern. Often times determining an outlier is a matter of judgment.

  10. EXAMPLE:Given the following data regarding exam scores and its histogram, describe the graph’s overall shape and identify any outliers. • the shape appears to be skewed to the left. • the score in the class 0 – 9, inclusive, could be considered an outlier.

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