Measures of Central Tendency

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Chapter 3 Measures of Central Tendency
I Mode A. Definition the Score or
Qualitative Category that Occurs With the
Greatest Frequency 1. Mode (Mo) for the
following data, number of required textbooks
for Freds four classes, is 2. 2 1 2 3
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Table 1. Taylor Manifest Anxiety
Scores _______________________________ (1) (2)

f
_______________________________ 74 1 73
1 72 0 71 2 70 7 Mo
69 69 8 68 5 67 2 66 1
65 1 _______________________________ n
28 _______________________________
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II Mean A. Definition the Mean Is the Sum of
Scores Divided by the Number of
Scores B. Formula
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C. Summation Operator, ??(Greek capitol sigma)?
D. Mean Formula for a Frequency
Distribution
1. k number of class intervals
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Table 2. Taylor Manifest Anxiety
Scores _________________ (1) (2) (3)
f
_________________ 74 1 74 73 1 73 72 0 0 7
1 2 142 70 7 490 69 8 552 68 5 340
67 2 134 66 1 66 65 1 65 _________________
n 28 1,936 _________________
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III Median (Mdn) A. Definition the Median
Divides Data Into Two Groups Having Equal
Frequency 1. If n is odd and the scores are
ordered, the median is the (n 1)/2th score
from either end of the number line. 2. If
n is even, the median is the midway point
between the n/2th score and the n/2
1th score from either end of the number line.
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B. Computational Examples
1. Determination of Mdn when n is odd
2. Determination of Mdn when n is even
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3. Determination of Mdn when n is even (a) or
odd (b), and the frequency of the middle
score value is greater than 1
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4. Determination of Mdn when n is even and the
frequency of the middle score value is
greater than 1
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C. Computation of Mdn for a Frequency
Distribution 1. Formula when scores are
cumulated from below
Xll real lower limit of the class
interval containing the median i
class interval size n number of
scores ??fb number of scores below
Xll fi number of scores in the class
interval containing the median
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2. Formula for the Mdn when scores are
cumulated from above
Xul real upper limit of class interval
containing the median ??fa number of
scores above Xul
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Table 3. Taylor Manifest Anxiety
Scores _____________________________
__________________________ 74 1 1 73 1 2 72 0
2 71 2 4 70 7 11 69 8 17 19 68 5 9 67 2 4 66 1
2 65 1 1 __________________________ n
28 __________________________
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IV Relative Merits of the Mean, Median, and
Mode V Location of the Mean, Median, and
Mode in a Distribution
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VI Mean of Two or More Means A. Weighted Mean
VII Summation Rules A. Sum of a Constant (c)
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B. Sum of a Variable (Vi)
C. Sum of the Product of a Constant and a
Variable
D. Distribution of Summation