Download Part I In the Beginning

Part II
Sigma Freud & Descriptive
Statistics
Chapter 2    
Means to an End:
Computing and Understanding Averages
What you will learn in Chapter 2
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Measures of central tendency
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Computing the mean and weighted mean for a set
of scores
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Computing the mode using the mode and the
median for a set of
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Selecting a measure of central tendency
Measures of Central Tendency
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The AVERAGE is a single score that best
represents a set of scores
Averages are also know as “Measure of
Central Tendency”
Three different ways to describe the
distribution of a set of scores…
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Mean – typical average score
Median – middle score
Mode – most common score
Computing the Mean
SX
X 
n

Formula for computing the mean

“X bar” is the mean value of the group of
scores
“S” (sigma) tells you to add together whatever
follows it
X is each individual score in the group
The n is the sample size
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Things to remember…
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N = population
n = sample
Sample mean is the measure of central
tendency that best represents the population
mean
Mean is VERY sensitive to extreme scores
that can “skew” or distort findings
Average means the one measure that best
represents a set of scores
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Different types of averages
Type of average used depends on the question
Weighted Mean Example
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List all values for which the mean is being
calculated (list them only once)
List the frequency (number of times) that
value appears
Multiply the value by the frequency
Sum all Value x Frequency
Divide by the total Frequency (total n size)
Weighted Mean Flying Proficiency Test(Salkind
p. 23)
Value
Frequency
Value*Freq
97
94
92
91
4
11
12
21
388
1,034
1,104
1,911
90
89
78
30
12
9
2,700
1,068
702
60
Total
1
100
60
8967
You Try!! Using Weighted Mean to Find Average
Super Bowl Yardage Penalty
Value
Frequency
5 (ie. False starts,
illegal downfield)
4
10 (offensive holding) 4
11 (Half the distance
penalties on
kickoffs/punts)
3
15 (personal fouls)
2
Value*Frequency
Computing the Median
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Median = point/score at which 50% of
remaining scores fall above and 50% fall
below.
NO standard formula

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Rank order scores from highest to lowest or
lowest to highest
Find the “middle” score
BUT…
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What if there are two middle scores?
What if the two middle scores are the same?
A little about Percentiles…

Percentile points are used to define the
percent of cases equal to and below a certain
point on a distribution

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75th %tile – means that the score received is at or
above 75 % of all other scores in the distribution
“Norm referenced” measure

allows you to make comparisons
Cumm Percentage of Ages (N=20)
Ages
freq
%
Cumm %
15-19
6
.30
.30
20-25
4
.20
.50
26-30
5
.25
.75
31-35
5
.25
1.00
Computing the Mode
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Mode = most frequently occurring score
NO formula
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List all values in the distribution
Tally the number of times each value occurs
The value occurring the most is the mode
Democrats = 90
Republicans = 70
Independents = 140 – the MODE!!
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When two values occur the same number of times
-- Bimodal distribution
Using Calculator
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Mode + . = statistical mode;
Shift +7= the mean “x-bar”
Shift +5= sum of x; square this value to get square
of the sum;
Shift +4 = sum of squares
Shift +9= sample standard deviation
Shift+1=permutations
Shift+2=combinations
When to Use What…
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Use the Mode
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Use the Median

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when the data are categorical
when you have extreme scores
Use the Mean

when you have data that do not include extreme
scores and are not categorical
Measures of Central Tendency
Choosing the right measure
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Normal distribution
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Mean: = median/mode
Median: = mean/mode
Mode: = mean/median
They all work.
Pick the one that fits the
need.
Chapter 3
15
Measures of Central Tendency
Choosing the right measure
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Positively skewed
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Mean: little high
Median: middle score
Mode: little low
Median works best
Chapter 3
16
Measures of Central Tendency
Choosing the right measure
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Negatively skewed
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Mean: too low
Median: middle score
Mode: little high
Median works best
Chapter 3
17
Central Tendencies and
Distribution Shape
Using SPSS
Glossary Terms to Know
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Average
Measures of Central Tendency
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Mean
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Median
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Weighted mean
Arithmetic mean
Percentile points
outliers
Mode