Transcript Descriptive Statistics

Descriptive Statistics
What’s in a number anyway?
Descriptive statistics
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Summarize a set of numbers in terms
of central tendency or variation
Foundational for inferential statistics
Measures of central
tendency
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Mean (µ)
Median
Mode
Normal Distribution
Thought Question
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Consider the following scores on a test
Marco 90
Chantelle 88
Chi Bo 92
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Adriane 85
Jay 45
Donnie 85
Linda 75
Remi 68
Christy 99
Marcus 97
Which measure of central tendency
would Adriane use when telling her
parents about her performance?
Thought Question
45 68 75 85 85 88 90 92 97 95
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Mode = 85 (most frequent score)
Mdn = 86.5 (score in middle of the
distribution)
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µ = 82.4 (average)
Thought Questions
If Jay scored an 85 instead of a 45, what
changes?
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Mode = 85 (most frequent score)
Mdn = 86.5 (score in middle of the distribution)
µ = 86 (average)
Highly deviant scores (called "outliers") have no
more effect on the median than those scores
very close to the middle. However, outliers
can greatly affect the mean.
An Extreme Example
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Consider the salaries of 10 people
Group A – All are teachers.
Salaries: $45,000
$50,000
$50,000
$55,000
$45,000
$50,000
$55,000
$45,000
$50,000
$55,000
An Extreme Example
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Consider the salaries of 10 people
Group B – Nine are teachers; 1 is
Donovan McNabb.
Salaries: $45,000
$45,000
$50,000
$50,000
$50,000
$55,000
$6,300,000
$45,000
$50,000
$55,000
An Extreme Example
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What happens to the mean and
median in these 2 examples? Does it
change?
What happens to the normal
distribution?
Positive Skew
Descriptive Statistics
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Frequency distributions
– Normal - scores equally distributed
around middle
– Positively skewed - large number of low
scores and a small number of high
scores; mean being pulled to the positive
– Negatively skewed - large number of high
scores and a small number of low scores;
mean being pulled to the negative
Negative Skew
Descriptive Statistics
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Variability
– How different are the scores?
– Two types
Range: the difference between the highest
and lowest scores
 Standard deviation
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– The average distance of the scores from the mean
– The relationship to the normal distribution
 ±1 SD = 68% of all scores in a distribution
 ±2 SD = 95% of all scores in a distribution
Standard Deviation
68%
95%
Variability
Variability
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Why does variability matter?
Next Class
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Read Orcher Ch.17,
Read Article (Muris & Meesters, 2002)
Think: What do correlations mean??