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Exploring Graphical Displays of Variables: Categorical and Quantitative Data

In this lecture, we discuss various graphical displays for both categorical and quantitative variables. For categorical data, we explore bar charts and pie charts. For quantitative data, we focus on histograms and stem-and-leaf plots to analyze center, spread, shape, and outliers. Additionally, we introduce time plots for variables measured over time, such as stock prices or rainfall amounts, with time plotted on the horizontal axis. This session emphasizes identifying patterns, trends, and significant deviations in data visualizations.

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Exploring Graphical Displays of Variables: Categorical and Quantitative Data

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  1. Stat 350, Lecture # 2 • We have talked about graphical displays of variables. • Categorical variables: Bar Chart and Pie chart. • Quantitative Variables: Histogram and to talk about center, spread and shape. • We have also taken a quick glance at outliers.

  2. More graphical displays for quantitative variables: • Stem and leaf plot: Quicker way for small data sets. Presents more detailed information and uses each individual observation. • Step1. Each observation has a leaf which is the final or rightmost digit . The remaining digits constitute the stem.

  3. For example if you have an observation of 345, 5 is the leaf and 34 is the stem. • Step 2: Write the stems in a vertical column with smallest at the top and draw a vertical line at the right of the column. • Step 3: Write ecah leaf in the row to the right of the stem in increasing order out from the stem.

  4. Stem and leaf for Automobile fuel economy: • Data: 25,26,29,24,26,29,30,28,28,29,27,28, 23,23,25,26,33,29,26,24,28,26,16,25,30 Minimum: 16 Maximum 33 1 6 2 3 3 4 4 5 5 5 6 6 6 6 6 7 8 8 8 9 9 3 0 0

  5. Time Plots (for variables measured over time) • Many variables are measured over time. E.g., Height of a child, price of a stock at the end of each day, amount of rainfall each year, unemployment rate each month.. • A time plot plots each observation against time at which it was measured. time is always on the horizontal scale and points are often connected by line.

  6. Example: Table 1.6 (Deaths from cancer over the years)

  7. Summary • Individuals and variables • Categorical and quantitative • Talk about variables through graphical displays. • Categorical Variable: Bar chart and pie chart • Quantitative: Histogram and stemplots • Variables recorded over time: Time plot

  8. Summary • Look for overall pattern and huge deviations from it. • Look at shape (symmetric, skewed) • Try to have an idea about center and spread • Look into outliers • In time plots look for trends.

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