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Part IISigma Freud Descriptive Statistics

• Chapter 2 ? ? ? ?
• Means to an End
• Computing and Understanding Averages

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What you will learn in Chapter 2

• Measures of central tendency
• Computing the mean and weighted mean for a set of
  scores
• Computing the mode using the mode and the median
  for a set of
• Selecting a measure of central tendency

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Measures of Central Tendency

• 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
• Mean typical average score
• Median middle score
• Mode most common score

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Computing the Mean

• Formula for computing the mean
• X bar is the mean value of the group of scores
• ? (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

• 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
• Different types of averages
• Type of average used depends on the question

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Weighted Mean Example

• 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)

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Weighted Mean Flying Proficiency Test(Salkind p.
23)
Value Frequency ValueFreq
97 4 388
94 11 1,034
92 12 1,104
91 21 1,911
90 30 2,700
89 12 1,068
78 9 702
60 1 60
Total 100 8967

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You Try!! Using Weighted Mean to Find Average
Super Bowl Yardage Penalty
Value Frequency ValueFrequency
5 (ie. False starts, illegal downfield) 4
10 (offensive holding) 4
11 (Half the distance penalties on kickoffs/punts) 3
15 (personal fouls) 2
Total


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Computing the Median

• Median point/score at which 50 of remaining
  scores fall above and 50 fall below.
• NO standard formula
• Rank order scores from highest to lowest or
  lowest to highest
• Find the middle score
• BUT
• What if there are two middle scores?
• What if the two middle scores are the same?

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A little about Percentiles

• Percentile points are used to define the percent
  of cases equal to and below a certain point on a
  distribution
• 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

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Cumm Percentage of Ages (N20)
Ages freq Cumm
15-19 6 .30 .30
20-25 4 .20 .50
26-30 5 .25 .75
31-35 5 .25 1.00


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Computing the Mode

• Mode most frequently occurring score
• NO formula
• 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!!
• When two values occur the same number of times --
  Bimodal distribution

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Using Calculator

• 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
• Shift1permutations
• Shift2combinations
• Shift3 factorials

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When to Use What

• Use the Mode
• when the data are categorical
• Use the Median
• when you have extreme scores
• Use the Mean
• when you have data that do not include extreme
  scores and are not categorical

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Measures of Central TendencyChoosing the right
measure

• Normal distribution
• Mean median/mode
• Median mean/mode
• Mode mean/median
• They all work.
• Pick the one that fits the need.

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Measures of Central TendencyChoosing the right
measure

• Positively skewed
• Mean little high
• Median middle score
• Mode little low
• Median works best

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Measures of Central TendencyChoosing the right
measure

• Negatively skewed
• Mean too low
• Median middle score
• Mode little high
• Median works best

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Central
Tendencies and
Distribution Shape
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Using SPSS
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Glossary Terms to Know

• Average
• Measures of Central Tendency
• Mean
• Weighted mean
• Arithmetic mean
• Median
• Percentile points
• outliers
• Mode