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Ch 3 Central Tendency

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Department
Management
Course Code
MGMT 1050
Professor
all

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Chapter 3 Central TendencyChapter Outline31 OverviewThe Reason for Measuring Central Tendency32 The MeanAlternative Definitions for the MeanThe Weighted MeanComputing the Mean from a Frequency Distribution TableCharacteristics of the Mean33 The MedianFinding the Median for Most DistributionsFinding the Precise Median for a Continuous VariableThe Median the Mean and the Middle34 The Mode35 Selecting a Measure of Central TendencyWhen to Use the MedianWhen to Use the ModeIn The LiteratureReporting Measures of Central Tendency Presenting Means and Medians in Graphs36 Central Tendency and the Shape of the DistributionSymmetrical DistributionsSkewed DistributionsInherit Learning Objectives and Chapter Summary1Students should understand the purpose of measuring central tendencyBecause central tendency serves two purposes identifying the center of the distribution and identifying the best representative score no single measure is always best for both purposesTherefore there are three methods for measuring central tendencyAt times one of the three measures is sufficient but occasionally two are three are used together to obtain a complete and accurate description of the distribution See Figure 31Instructor NotesChapter 3page 322Students should be able to define and compute each of the three measures of central tendency It may seem obvious but remind students that two values are needed to compute the mean the number of scores and the sum of the scoresThey need to obtain both of these values before the mean can be computedMost students find that the median and the mode are easier to compute if a distribution is displayed in a frequency distribution histogram3Students should understand how the mean is affected when a set of scores is modified a new score is added a score is removed or a score is changedBefore attempting to compute the mean students should be able to visualize what is going to happenRemind them that the mean is the balance point and they can visualize the original distribution as a set of blocks on a seesaw that is balanced at the meanThe modification involves adding a new block taking away a block or moving a blockIn any case they should be able to see how the modification affects the balanceAgain the key to calculating the mean is to find the number of scores n and the sum of the scores XStudents first need to determine exactly how the modification affects the number of scoresThen they must determine how the modification affects the sum of the scoresOnce these two values are determined the mean is easy4Students should understand the circumstances in which each of the three measures of central tendency is appropriateMost of the time the mean is the preferred measure especially if the scores are numerical valuesThe median is most commonly used in situations where the mean can be calculated but the calculated value is not a good representative scoreTypically this occurs with skewed distributions or when a distribution has a few extreme scores often called outliersThe mode is the only measure available for nonnumerical nominal dataIt also is used as a supplemental measure along with the mean to help describe the shape of a distribution5Students should understand how the three measures of central tendency are related to each other in symmetrical and skewed distributionsOf the three measures the mean is the one that is most affected by extreme scoresThus the mean is displaced toward the extreme scores in the tail of a skewed distributionIf you begin with a skewed distribution and change a score in the tail so that it becomes even more extreme only the mean will be affected by the changeInstructor NotesChapter 3page 33
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