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Graphical Displays of Data

Graphical Displays of Data. Section 2.2. Objectives. Create and interpret the basic types of graphs used to display data. Introduction. A graph is a snapshot that allows us to view patterns at a glance without undergoing lengthy analysis of the data.

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Graphical Displays of Data

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  1. Graphical Displays of Data Section 2.2

  2. Objectives • Create and interpret the basic types of graphs used to display data

  3. Introduction • A graph is a snapshot that allows us to view patterns at a glance without undergoing lengthy analysis of the data. • Graphs are much more visually appealing than a table or list. • A graph should be able to stand alone, without the original data. Graph must be given a title, as well as labels for both axes.

  4. Purpose of Statistical Graphs • To convey the data to the viewers in pictorial form • It is easier for most people to comprehend the meaning of data presented as a picture than data presented as a table. This is especially true if the viewers have little or no statistical knowledge • To describe the data set • To analyze the data set (Distribution of data set) • To summarize a data set • To discover a trend or pattern in a situation over a period of time • To get the viewers’ attention in a publication or speaking presentation

  5. Graphs Used to Display Qualitative Data

  6. Pie Chart • Pie Chart is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution. • Show relationship of the parts to the whole

  7. Pareto Chart* • Bar graph • Used to represent a frequency distribution for a categorical variable (nominal level) and the frequencies are displayed by the heights of the contiguous vertical bars, which are arranged in order from highest to lowest.

  8. How do I create a Pareto Chart from a categorical frequency distribution? • STEP 1: Draw the x- and y-axes • STEP 2: Label the x-axis using the qualitative categories (highest frequency to lowest frequency) • STEP 3: Label the y-axis using an appropriate scale that encompasses the high and low frequencies • STEP 4: Draw the contiguous vertical bars

  9. Example

  10. Other Bar Graphs Side-by-Side Bar Graph Stacked Bar Graph • Used to compare different groups • Typically, uses different colored bars to distinguish groups

  11. Histogram* • A bar graph that displays the data from a frequency distribution • Horizontal Scale (x-axis) is labeled using CLASS BOUNDARIES or MIDPOINTS • Vertical Scale (y-axis) is labeled using frequency • NOTE: bars are contiguous (No gaps)

  12. How do I create a histogram from a grouped frequency distribution? • MINITAB • Enter raw data into MINITAB

  13. Example-Construct a histogram of the ages of Nextel Cup Drivers. Use the class boundaries as the scale on the x-axis

  14. Frequency Polygon • Line graph (rather than a bar graph) • Uses class midpoints rather than class boundaries on x-axis

  15. Ogive (Cumulative Frequency Polygon) • Line graph (rather than a bar graph) • Uses class boundaries on x-axis • Uses cumulative frequencies (total as you go) rather than individual class frequencies • Used to visually represent how many values are below a specified upper class boundary

  16. Another possibility • We can use the percentage (relative frequency) rather than the “tallies” (frequency) on the x-axis. • Relative Frequency Histogram • Relative Frequency Polygon • Relative Frequency Ogive • Used when a comparison between two data sets is desired, especially if the data sets are two different sizes • Overall shape (distribution) of graph is the same, but we use a % on the y-axis scale

  17. Stem and Leaf Plot* • Method for organizing data • Combination of sorting and graphing • Original Data is retained unlike with a grouped frequency distribution • “Leaves” are usually the last digit in each data value; right hand column of two-column table • “Stems” are remaining digits ; left hand column of two-column table

  18. Dotplot*(not in text) • Graph in which each data value is plotted as a point (or dot) along a single horizontal scale of values. • Dots representing equal values are stacked • Original data is retained

  19. Exam #1 Scores in Mrs. Ralston’s Math 1111 classes in Fall 2008

  20. Construct a frequency distribution for the Exam #1 scores. Use 8 classes with a class width of 10 beginning with a lower class limit of 30. • Use the raw data to construct a histogram of the Exam #1 scores in MINITAB • Use the raw data to construct a dotplot of the Exam #1 scores in MINITAB

  21. Homework • Page 71 #2 and 3 (create a Pareto Chart) • Page 74 #16 (create a Stem and Leaf Plot) • Worksheet

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