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Part IIigma Freud & Descriptive Statistics
Chapter 2
Means to an End:
Computing and Understanding Averages
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
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
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
XX
n
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
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)
Weighted Mean Flying Proficiency Test(Salkind p. 23)
Value Frequency Value*Freq
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
You Try!! Using Weighted Mean to Find Average Super Bowl Yardage Penalty
Value Frequency 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
Total
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?
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
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 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 = 90Republicans = 70Independents = 140 – the MODE!!
When two values occur the same number of times -- Bimodal distribution
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 Shift+1=permutations Shift+2=combinations Shift+3= factorials
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
Chapter 3 15
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.
Chapter 3 16
Measures of Central TendencyChoosing the right measure
Positively skewed Mean: little high Median: middle score Mode: little low
Median works best
Chapter 3 17
Measures of Central TendencyChoosing the right measure
Negatively skewed Mean: too low Median: middle score Mode: little high
Median works best
Central Tendencies and Distribution Shape
Using SPSS
Glossary Terms to Know Average Measures of Central Tendency
Mean Weighted mean Arithmetic mean
Median Percentile points outliers
Mode