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Ch 2 Frequency and Distributions

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York University
MGMT 1050

Chapter 2 Frequency DistributionsChapter Outline21 Introduction to Frequency Distributions22 Frequency Distribution TablesObtaining X from a Frequency Distribution TableProportions and PercentagesGrouped Frequency Distribution TablesReal Limits and Frequency Distributions23 Frequency Distribution GraphsGraphs for Interval or Ratio Data Histograms and PolygonsGraphs for Nominal or Ordinal Data Bar GraphsGraphs for Population Distributions Relative Frequencies and Smooth Curves24 The Shape of a Frequency Distribution25 Percentiles Percentile Ranks and InterpolationCumulative Frequency and Cumulative PercentageInterpolation26 Stem and Leaf DisplaysComparing Stem and Leaf Displays with Frequency DistributionsLearning Objectives and Chapter Summary1Students should understand the concept of a frequency distribution as an organized display showing where all of the individual scores are located on the scale of measurement Note that one goal of descriptive statistics is to organize research results so that researchers can see what happenedAlso note that a frequency distribution does not simply summarize the scores but rather shows the entire set of scores2Students should be able to organize data into a regular or a grouped frequency distribution table and understand data that are presented in a tableIf scores are presented in a regular table students should be able to retrieve the complete list of original scoresThe purpose for a grouped table is to keep the presentation relatively simple and easy to understandAll of the guidelines for constructing a grouped table are intended to help make the result easy and simpleNote however that after the scores have been put into a grouped table the individual score values are lostInstructor NotesChapter 2page 163Students should be able to organize data into frequency distribution graphs including bar graphs histograms and polygonsAlso students should be able to understand data that are presented in a graphBar graphs space between bars are used to display data from nominal and ordinal scalesPolygons and histograms are used for data from interval or ratio scalesIf scores are presented in a frequency distribution graph students should be able to retrieve the complete list of original scores4Students should understand that most population distributions are drawn as smooth curves showing relative proportions rather than absolute frequencies5Students should be able to identify the shape of a distribution shown in a frequency distribution graphStudents should recognize symmetrical distributions including but not limited to normal distributions as well as positively and negatively skewed distributions 6Students should be able to describe locations within a distribution using percentiles and percentile ranks and they should be able to compute percentiles and ranks using interpolation when necessary The first key to determining percentiles and percentile ranks is the idea that all cumulative values both frequencies and percentages correspond to the upper real limit of each intervalThe process of interpolation is based on two concepts1Each interval is defined in terms of two different scales scores and percentagesIn Example 27 for example one interval extends from X45 to X95 in terms of scores and the same interval extends from 10 to 60 in terms of percentages2 A fraction of the interval on one scale corresponds to exactly the same fraction of the interval on the other scaleFor example a score of X7 is exactly halfway between 45 and 95 and the corresponding value of 35 is exactly halfway between 10 and 60Other Lecture Suggestions1Begin with an unorganized list of scores as in Example 21 and then organize the scores into a tableIf you use a set of 20 or 25 scoresit will be easy to compute proportions and percentages for the same example2Present a relatively simple regular frequency distribution table for example use scores of 5 4 3 2 and 1 with corresponding frequencies of 1 3 5 3 2Ask the students to determine the values of N and X for the scoresNote that X can be obtained two different ways 1 by computing and summing the fX values within the table 2 by retrieving the complete list of individual scores and working outside the tableInstructor NotesChapter 2page 17
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