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Chapter 2

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2.1 Frequency Distributions 2.2 Graphical Displays of Data 2.3 Analyzing Graphs

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After collecting data as described in Chapter 1, you need to organize it so that inferences and conclusions can be drawn Raw data is not very meaningful to an audience. Additionally, in our modern, fast paced society, graphs are useful for quickly providing a wealth of information to an audience.

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Objectives ◦ Determine how to construct a frequency table

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A frequency distribution is the organization of raw data in table form, using classes (groups) and frequencies ◦ Class (group) is a quantitative or qualitative category ◦ Frequency, f, of a class is the number of data values contained in a specific class

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Categorical Frequency Distribution Grouped Frequency Distribution Used for data that can be used in specific categories, such as nominal or ordinal level data. ◦ Examples: Political affiliations, religious affiliations, major field of study Used with quantitative data Classes (groups) included more than one unit of measurement

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Make a table Tally the data Count the tallies Find percentage of values in each class using the following formula: % = Find the grand totals for frequency & percent ClassTallyFrequencyPercent

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NursingBusiness AdminEducation Computer Info Systems Political ScienceArt General StudiesNursingEducation PsychologyBusiness Admin PsychologyBusiness AdminGeneral Studies History General Studies EducationComputer Info Systems Nursing EducationGeneral StudiesEducation History

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Definitions ◦ Lower Class Limit (LCL) is the smallest data value that can be included in the class ◦ Upper Class Limit (UCL) is the largest data value that can be included in the class ◦ Class Boundaries are used to separate the classes so that there is no gaps in the frequency distribution Rule of Thumb: Have one additional place value and end in.5 Find class boundaries by subtracting 0.5 from each LCL and adding 0.5 to each UCL ◦ Class Width is the difference between two consecutive LCL Find by subtracting LCL 2 –LCL 1

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We must decide how many classes to use and the width of each class using the following guidelines: ◦ There should be between 5 and 20 classes. ◦ It is preferable, but not absolutely necessary that the class width be an odd number ◦ The classes must be mutually exclusive (nonoverlapping values) ◦ The classes must be continuous (no gaps, even if frequency is 0) ◦ The classes must be exhaustive (use all the data) ◦ The classes must be equal in width

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Decide on the number of classes (given) Determine the class width (given) Select a starting point (this is the first LCL) (given) Determine the LCL by adding the class width to first LCL to determine next LCL, ….. Determine the UCL by subtracting 1 from second LCL to obtain first UCL, then add class width to determine next UCL….. Tally the data

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Find the numerical frequencies from tallies Find the grand total of frequency Class LimitsClass Boundaries TallyFrequency

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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

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To organize data in a meaningful, intelligible way To enable the reader to determine the nature or shape of the distribution To facilitate computational procedures for measures of average and spread To enable us to draw charts and graphs for the presentation of data To enable the reader to make comparisons among different data sets

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Page 57 #15-18 (You do not have to identify class boundary, class midpoint, relative frequency, or cumulative frequency!!!) Only two or three column table ---column 1: Class, column 2: tally, column 3: frequency

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