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Graphical Displays of Data Section 2.2

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

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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.

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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

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Graphs Used to Display Qualitative Data

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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

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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.

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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

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Example NursingBusiness AdminEducation Computer Info SystemsPolitical ScienceArt General StudiesNursingEducation PsychologyBusiness Admin PsychologyBusiness AdminGeneral Studies History General Studies EducationComputer Info SystemsNursing EducationGeneral StudiesEducation History

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Class (Major)FrequencyPercentage Art13.6% Business Administration 310.7% Computer Info Systems 27.1% Education621.4% General Studies621.4% History414.3% Nursing310.7% Political Science13.6% Psychology27.1% TOTAL28100%

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

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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)

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

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Ages of NASCAR Nextel Cup Drivers in Years (NASCAR.com) (Data is ranked---Collected Spring 2008) 21 23 2425 26 27 28 29 30 31 323435 36 37 38 394142 43 44 45 464748 49 50 51 6572 Example-Construct a histogram of the ages of Nextel Cup Drivers. Use the class boundaries as the scale on the x-axis

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

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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

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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

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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

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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

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Exam #1 Scores in Mrs. Ralston’s Math 1111 classes in Fall 2008 39 4041435059 616364 65 66 6870 7173 75 76777879 80 81 828384 8586 878889 90 91 9294 9596 98 99 100

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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

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

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