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Canada (510,370)
QMS 102 (186)
Clare Chua (18)

Module 3.pdf

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Quantitative Methods
QMS 102
Clare Chua

30012013Blackboard LearnLearning ObjectivesBy the end of this module you will be able to 1 Construct a frequency distribution 2 Construct a relative frequency distribution3 Construct a percentage frequency distribution tableWhat is a Frequency DistributionA frequency distribution is a table that grouped the raw data of quantitative type into class intervals or rangeof valuesExample Frequency Distribution of marks of a statistics testNumber ofMarks of a statistics test students 0 and under 20520 and under 40240 and under 60860 and under 801080 and under 10015Some terminologies that you need to know about the frequency distribution 1 What is Class interval Class intervals are ranges of values having equal widths For example 0 and under 20 is the first class 20and under 40 is the second class 40 and under 60 is the third class 60 and under 80 is the fourth classand 80 and under 100 is the fifth classThere are several possible notations that are used to designate the classesIn this course you will use theand under notation eg 20 and under 402 What is Class width Class width denotes as CW is the difference between the upper and lower boundaries of any class Theclass width is determined by the formulaCWUpper boundarylower boundaryExample CW402020 3 What is BoundariesThe numerical values used in designating the classes when using the and under notation are calledboundarieshttpscoursesryersoncawebappsportalframesetjsptabtabgroupid151url2Fwebapps2Fblackboard2Fexecute2Flauncher3Ftype3DCou12030012013Blackboard Learn4 What is Upper BoundariesThe maximum value of a class interval is called the upper boundaries The upper boundary of one classbecomes a lower boundary of the next class There is no gap between the upper boundary of one class andthe lower boundary of the next class5 What is Lower BoundariesThe minimum value of a class interval is called the lower boundaries6 What is Frequency Number of data values which fall inside a class Rules to construct a Frequency DistributionPlease follow these rules to construct a Frequency Distribution 1 Classes There are several possible notations that are used to designate the classesIn this courseyou will use the and under notation eg 10 and under 202 Number of classes The number of classes you should use is between 5 and 10 classes Usually asmaller number of classes for small data sets and a larger number of classes for large data sets 3 Class width CW You are recommended to use a nice number to construct the class intervals Therecommended class widths are shown in the table below You start with a list of nice numbers 1 2 25and 5 If you need a larger class widths you multiple each number In this list 12 25 5 by 10 1 x 102x 10 25 x 10 5 x 10 to get another list of numbers 10 20 25 and 50 If you need a smaller classwidth you divide each number in this list 12255 by 10 110 210 2519 510 to get another listof numbers 01 02 025 054 Class width CW In this course when you are asked to make a frequency distribution all classesmust have the same class width 5 Boundaries There are several guidelines that should be used to determine the actual numericalvalues of the boundariesa Boundaries should look like the data ie have the same number of decimal places as the data For example if the raw data have one decimal then the boundaries should have one decimalbEach boundary should be a multiple of the chosen class widthc Boundaries must be no gaps between the classes ie the upper boundary of one class will alsobe the lower boundary of the next classd The first and last classes should not have zero frequencies6 FrequencyNumber of data values which fall inside a class The heading should indicate what is beinghttpscoursesryersoncawebappsportalframesetjsptabtabgroupid151url2Fwebapps2Fblackboard2Fexecute2Flauncher3Ftype3DCou220
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