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Chapter 11

Chapter 11. STA 200 Summer I 2011. Histograms. Bar graphs and pie charts are appropriate graphs for categorical variables. To display the distribution of a quantitative variable graphically, we use a histogram.

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Chapter 11

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  1. Chapter 11 STA 200 Summer I 2011

  2. Histograms • Bar graphs and pie charts are appropriate graphs for categorical variables. • To display the distribution of a quantitative variable graphically, we use a histogram. • In most cases, quantitative variables take way too many values to have a separate bar for each value. • Instead, we’ll have to group values together into intervals, or classes.

  3. Creating a Histogram • Divide the range of data into classes of equal width. Then, count the number of individuals in each class. • When drawing the histogram: • the variable goes on the horizontal axis • the rate or count of occurrences goes on the vertical axis • the height of each bar is determined by the rate or count of occurrences • the bars should touch

  4. Example • Suppose we have the following exam grades:

  5. Example (cont.) • Step 1: Choosing Classes • Make sure all of your classes are the same size. • Make sure your classes cover all of the data. • Make sure that none of your classes overlap. • Here, we’re going to set up the classes in the most accessible manner: • 90-99 • 80-89 • 70-79 • etc.

  6. Example (cont.) • Step 2: Counting

  7. Example (cont.) Histogram:

  8. Things to Look For • Outliers: • observations outside the overall pattern of data • either significantly higher or significantly lower than the rest of the data • Shape • roughly symmetric, left-skewed, or right-skewed

  9. Outliers • In the exam score example, are there any outliers? • In a histogram, the outliers will usually stand out:

  10. Shape • If a distribution is roughly symmetric, the left and right sides will be approximate mirror images of each other. • If a distribution is skewed, one tail will be longer than the other. • left-skewed: long left tail • right-skewed: long right tail

  11. More Shape • Some types of data regularly produce distributions with a specific shape. • Symmetric (not necessarily bell-shaped): the size of organisms of the same species, IQ scores • Right-skewed: income • Left-skewed: exam scores (usually)

  12. Stem-and-Leaf Plots • A quick, easy alternative to a histogram is a stem-and-leaf plot. • For small data sets, a stem-and-leaf plot may be preferable to a histogram: • stem-and-leaf plots are quicker to make • they show more information than a histogram

  13. Constructing a Stem-and-Leaf Plot • Separate each observation into a stem and a leaf. • The leaf is the final digit. • The stem is everything but the final digit. • Write the stems in a vertical column with the smallest one on top. • Write each leaf in the row next to the appropriate stem. The leaves in each row should increase as you get farther away from the stem. • If you have to round off the observations, be sure to use a key or legend to explain the rounding.

  14. Example • The following data represent the salaries (in millions) of a major league baseball team: • Create a stem-and-leaf plot of the data.

  15. Example (cont.) Stem Leaf What shape does the distribution have?

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