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MGMT 1050 Study Guide - M60 Patton, Level Of Measurement, Central Tendency

by OneClass280301 , Fall 2013
15 Pages
54 Views
Fall 2013

Department
Management
Course Code
MGMT 1050
Professor
all

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Chapter 3: Central Tendency
Chapter Outline
3.1 Overview (The Reason for Measuring Central Tendency)
3.2 The Mean
Alternative Definitions for the Mean
The Weighted Mean
Computing the Mean from a Frequency Distribution Table
Characteristics of the Mean
3.3 The Median
Finding the Median for Most Distributions
Finding the Precise Median for a Continuous Variable
The Median, the Mean, and the Middle
3.4 The Mode
3.5 Selecting a Measure of Central Tendency
When to Use the Median
When to Use the Mode
In The Literature: Reporting Measures of Central Tendency
Presenting Means and Medians in Graphs
3.6 Central Tendency and the Shape of the Distribution
Symmetrical Distributions
Skewed Distributions
Inherit
Learning Objectives and Chapter Summary
1. Students should understand the purpose of measuring central tendency.
Because 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
purposes. Therefore, there are three methods for measuring central tendency. At 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 3.1).
Instructor Notes – Chapter 3 – page 32
2. Students 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 scores. They need to obtain both of these
values before the mean can be computed. Most students find that the median and the
mode are easier to compute if a distribution is displayed in a frequency distribution
histogram.
3. Students 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 changed).
Before attempting to compute the mean, students should be able to visualize what is
going to happen. Remind them that the mean is the balance point and they can visualize
the original distribution as a set of blocks on a see-saw that is balanced at the mean. The
modification involves adding a new block, taking away a block, or moving a block. In
any case, they should be able to see how the modification affects the balance.
Again, the key to calculating the mean is to find the number of scores (n) and the sum of
the scores (ΣX). Students first need to determine exactly how the modification affects the
number of scores. Then, they must determine how the modification affects the sum of
the scores. Once these two values are determined, the mean is easy.
4. Students should understand the circumstances in which each of the three measures of central
tendency is appropriate.
Most of the time, the mean is the preferred measure, especially if the scores are numerical
values. The median is most commonly used in situations where the mean can be
calculated but the calculated value is not a good representative score. Typically, this
occurs with skewed distributions or when a distribution has a few extreme scores (often
called outliers). The mode is the only measure available for non-numerical (nominal)
data. It also is used as a supplemental measure (along with the mean) to help describe the
shape of a distribution.
5. Students should understand how the three measures of central tendency are related to each
other in symmetrical and skewed distributions.
Of the three measures, the mean is the one that is most affected by extreme scores. Thus,
the mean is displaced toward the extreme scores in the tail of a skewed distribution. If
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 change.
Instructor Notes – Chapter 3 – page 33
6. Students should be able to draw and to understand figures/graphs that display several different
means (or medians) representing different treatment conditions or different groups.
Line graphs are typically used when the treatment conditions or groups correspond to
numerical values (interval or ratio scales). Otherwise, bar graphs are used to display the
means.
Other Lecture Suggestions
1. The mean can be introduced as the “average” that students already know how to calculate.
For example, ask students to find the average telephone bill if one month is $20 and the next
month is $30. Everyone gets this right. Now, add a third month with a bill of $100. Many
students will tell you that the mean is now $75. This is a good chance to introduce the formula
for the mean, showing that the total cost (ΣX = $150) is divided over three (n = 3) months.
2. Sketch a simple histogram and label the values along the X axis using 1, 2, 3, 4, and 5. Ask
the students what will happen to the distribution if you add 10 points to every score. Answer:
The whole distribution moves 10 points to the right. (You can keep the same sketch, simply re-
label the values on the X axis to 11, 12, 13, 14, and 15.) Note that the mean (middle) has shifted
10 points to the right.
Go back to the original distribution and ask what would happen if every score were
multiplied by 10. This time the 1s become 10s, the 2s become 20s, and so on. Again, you can
keep the same sketch, simply re-label the values on the X axis to 10, 20, 30, 40, and 50. After
multiplying, the mean (that used to be at 3) is located at 30 (10 times bigger).
3. The idea that the mean is not always a central, representative value can be demonstrated by
starting with a simple, symmetrical distribution consisting of scores 1, 2, 3, 4, and 5 with
frequencies of 1, 2, 4, 2, and 1, respectively. Just looking at the frequency distribution
histogram, it is easy to see that the mean is 3, but you can also demonstrate that the n = 10 scores
add up to ΣX = 30.
Now, move the score at X = 5 to a new location at X = 55 and have students find the new
mean (adding 50 points to one score adds 50 points to the total, so ΣX is now 80 and the mean is
8). Note that the new mean, 8, is not a representative value. In fact, none of the scores is located
around X = 8. Finally, you can introduce the median using the original distribution (Median = 3)
and then see what happens to this measure of central tendency when X = 5 is moved to X = 55
(the median is still 3). The median is relatively unaffected by extreme scores.
Instructor Notes – Chapter 3 – page 34

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Description
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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