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Describing Data Visually

Chapter Contents 3.1 Visual Description 3.2 Dot Plots 3.3 Frequency Distributions and Histograms 3.4 Excel Charts 3.5 Line Charts 3.6 Bar Charts 3.7 Scatter Plots 3.8 Tables 3.9 Pie Charts 3.10 Deceptive Graphs. Describing Data Visually. Chapter 3.

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Describing Data Visually

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  1. Chapter Contents 3.1 Visual Description 3.2 Dot Plots 3.3 Frequency Distributions and Histograms 3.4 Excel Charts 3.5 Line Charts 3.6 Bar Charts 3.7 Scatter Plots 3.8 Tables 3.9 Pie Charts 3.10 Deceptive Graphs Describing Data Visually Chapter 3

  2. Chapter Learning Objectives (LO’s) LO1:Make a dot plot by hand or by computer. LO2: Create a frequency distribution for a data set. LO3:Make a histogram with appropriate bins. LO4:Identify skewness, modes, and outliers in a histogram. LO5: Make an effective line chart using Excel. LO6:Make and interpret a scatter plot using Excel. LO7:Know the rules for effective bar charts and pie charts. LO8:Make simple tables and pivot tables. LO9:Recognize deceptive graphing techniques. Describing Data Visually Chapter 3

  3. 3.2 Dot Plots LO1 Chapter 3 • Methods of organizing, exploring and summarizing data include: • Visual (charts and graphs) provides insight into characteristics of a data set without using mathematics. • Numerical(statistics or tables) provides insight into characteristics of a data set using mathematics. LO1:Make a dot plot by hand or by computer • A dot plot is the simplest graphical display of n individual values of numerical data. - Easy to understand - Not good for large samples (e.g., > 5,000). • Steps in Making a Dot Plot 1. Make a scale that covers the data range 2. Mark the axes and label them 3. Plot each data value as a dot above the scale at its approximate location Note: If more than one data value lies at about the same axis location, the dots are piled up vertically.

  4. 3.2 Dot Plots LO1 Chapter 3 • Range of data shows dispersion. • Clustering shows central tendency. • Dot plots do not tell much about the shape of distribution.

  5. 3.2 Dot Plots LO1 Chapter 3 Comparing Groups • A stacked dot plotcompares two or more groups using a common X-axis scale.

  6. 3.3 Frequency Distributions and Histograms LO2 Chapter 3 LO2: Create a Frequency Distribution for a Data Set Bins and Bin Limits • A frequency distributionis a table formed by classifying n data values into k classes (bins). • Bin limitsdefine the values to be included in each bin. Widths must all be the same. • Frequencies are the number of observations within each bin. • Expressas relative frequencies(frequency divided by the total) or percentages (relative frequency times 100).

  7. 3.3 Frequency Distributions and Histograms LO3 Chapter 3 LO3:Make a histogram with appropriate bins. Histograms • A histogram is a graphical representation of a frequency distribution. Y-axis shows frequency within each bin. • A histogram is a bar chart. X-axis ticks shows end points of each bin. One can use appropriate technology to construct histograms

  8. 3.3 Frequency Distributions and Histograms LO4 Chapter 3 LO4:Identify skewness, modes, and outliers in a histogram . Skewed right? Skewed left? Symmetrical?

  9. 3.3 Frequency Distributions and Histograms LO4 Chapter 3 More skewedness

  10. 3.3 Frequency Distributions and Histograms LO4 Chapter 3 More skewedness

  11. 3.3 Frequency Distributions and Histograms LO4 Chapter 3 Frequency Polygons and Ogives 3.4 EXCEL CHARTS This section describes how to use Excel to create charts.

  12. 3.5 Line Charts LO5 Chapter 3 LO5:Make an effective line chart using Excel. Simple Line Charts • Used to display a time series or spot trends, or to compare time periods. • Can display several variables at once.

  13. 3.5 Line Charts LO5 Chapter 3 Simple Line Charts • Two-scale line chart – used to compare variables that differ in magnitude or are measured in different units.

  14. 3.5 Line Charts LO5 Chapter 3 Log Scales • Useful for time series data that might be expected to grow at a compound annual percentage rate (e.g., GDP, the national debt, or your future income). It reveals whether the quantity is growing at an increasing percent (concave upward), constant percent(straight line), or declining percent (concave downward)

  15. 3.6 Bar Charts LO7 Chapter 3 LO7: Know the rules for effective bar charts and pie charts. Simple Bar Charts • Most common way to display attribute data. - Bars represent categories or attributes. - Lengths of bars represent frequencies. Vertical Bar Chart Horizontal Bar Chart

  16. 3.6 Bar Charts LO7 Chapter 3 Pareto Charts • Special type of bar chart used in quality management to display the frequency of defects or errors of different types. • Categories are displayed in descending order of frequency. • Focus on significant few(i.e., few categories that account for most defects or errors).

  17. 3.6 Bar Charts LO7 Chapter 3 Bar Charts for Time Series Data • Bar charts can be used for time series data although it may be harder to compare trends.

  18. 3.7 Scatter Plots LO6 Chapter 3 LO6: Make an interpret a scatter plot using Excel. • Scatter plots can convey patterns in data pairs that would not be apparent from a table.

  19. 3.8 Tables LO8 Chapter 3 LO8:Make simple tables and Pivot tables • Tablesare the simplest form of data display. • A compound tableis a table that contains time series data down the columns and variables across the rows. Here are some tips for creating effective tables: 1. Keep the table simple, consistent with its purpose. Put summary tables in the main body of the written report and detailed tables in an appendix. 2. Display the data to be compared in columns rather than rows. 3. For presentation purposes, round off to three or four significant digits. 4. Physical table layout should guide the eye toward the comparison you wish to emphasize. 5. Row and column headings should be simple yet descriptive. 6. Within a column, use a consistent number of decimal digits.

  20. 3.8 Tables LO8 Chapter 3 Example: School Expenditures • Units of measure are stated in the footnote. • Note merged headings to group columns. • See text for “Tips for Effective Tables”.

  21. 3.9 Pie Charts LO7 Chapter 3 LO7:Know the rules for effective bar charts and pie charts An Oft-Abused Chart • A pie chart can only convey a general idea of the data. • Pie charts should be used to portray data which sum to a total (e.g., percent market shares). • A pie chart should only have a few (i.e., 2 or 3) slices. • Each slice should be labeled with data values or percents.

  22. 3.10 Deceptive Graphs LO9 Chapter 3 LO9: Recognize deceptive graphing techniques • Error 1:Nonzero Origin • Error 2:Elastic Graph Proportions • Error 3:Dramatic Title • Error 4:Distracting Pictures • Error 5:Authority Figures • Error 6:3-D and Rotated Graphs • Error 7:Missing Axis Demarcations • Error 8:Missing Measurement Units or Definitions • Error 9:Vague Source • Error 10:Complex Graphs • Error 11:Gratuitous Effects • Error 12:Estimated Data • Error 13:Area Trick

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