Download Stats for AP Psych - District 196 e

Basic Statistics
AP Psychology
Outline
I. Introduction
II. Measures of central tendency
a.
b.
c.
Mean
Median
Mode
III. Measures of variance
a.
b.
c.
Range
Variance
Standard Deviation
IV. Normal distribution, empirical rule, and skewed
distributions
Distributions
• A distribution is a set of outcomes (e.g. scores)
• A distribution can be represented graphically
using a histogram and distribution curve:
Exercise
Roll three dice 100 times and record the
outcomes on a histogram
Exercise
Roll three dice 100 times and record the
outcomes on a histogram
• What do you notice about the distribution?
• How would you describe the distribution to
someone else?
Exercise
Roll three dice 100 times and record the
outcomes on a histogram
• What do you notice about the distribution?
• How would you describe the distribution to
someone else?
Describing a Distribution
A distribution can be described using…
Describing a Distribution
A distribution can be described using…
measures of central tendency (a single score
that represents the whole set of scores),
and…
Describing a Distribution
A distribution can be described using…
measures of central tendency (a single score
that represents the whole set of scores),
and…
measures of variance (how similar or diverse
the scores are)
Measures of Central Tendency
Measures of Central Tendency describe a set of
scores as a single number
Measures of Central Tendency
Measures of Central Tendency describe a set of
scores as a single number
• Mean = Average score
Measures of Central Tendency
Measures of Central Tendency describe a set of
scores as a single number
• Mean = Average score
• Median = 50th percentile (middle score)
Measures of Central Tendency
Measures of Central Tendency describe a set of
scores as a single number
• Mean = Average score
• Median = 50th percentile (middle score)
• Mode = Most common score
Mean
Mean: Average of the scores
Example: 1, 4, 7
Mean = (1+4+7)/3 = 12/3 = 4
Note: The Mean is a good measure of central
tendency but can be skewed by outliers
Mean
Mean: Average of the scores
Example: 1, 4, 7
Mean = (1+4+7)/3 = 12/3 = 4
Note: The Mean is a good measure of central
tendency but can be skewed by outliers
Mean
Mean: Average of the scores
Example: 1, 4, 7
Mean = (1+4+7)/3 = 12/3 = 4
Note: The Mean is a good measure of central
tendency but can be skewed by outliers
Median
Median: 50th percentile (middle score)...
–
–
–
–
Half of the scores are above it and half are below it
If there is an odd number of scores, take the middle score
If there is even number of scores, average the two middle scores
You can find the middle score using this formula: (n+1)/2
Example: 1, 4, 7
Median = 2nd score = 4
(n+1)/2 = (3+1)/2 = 2nd score
Example: 1, 3, 5, 7
Median = average of 2nd and 3rd scores = 4
Median
Median: 50th percentile (middle score)...
–
–
–
–
Half of the scores are above it and half are below it
If there is an odd number of scores, take the middle score
If there is even number of scores, average the two middle scores
You can find the middle score using this formula: (n+1)/2
Example: 1, 4, 7
Median = 2nd score = 4
(n+1)/2 = (3+1)/2 = 2nd score
Example: 1, 3, 5, 7
Median = average of 2nd and 3rd scores = 4
Median
Median: 50th percentile (middle score)...
–
–
–
–
Half of the scores are above it and half are below it
If there is an odd number of scores, take the middle score
If there is even number of scores, average the two middle scores
You can find the middle score using this formula: (n+1)/2
Example: 1, 4, 7
Median = 2nd score = 4
(n+1)/2 = (3+1)/2 = 2nd score
Example: 1, 3, 5, 7
Median = average of 2nd and 3rd scores = 4
Median
Median: 50th percentile (middle score)...
–
–
–
–
Half of the scores are above it and half are below it
If there is an odd number of scores, take the middle score
If there is even number of scores, average the two middle scores
You can find the middle score using this formula: (n+1)/2
Example: 1, 4, 7
Median = 2nd score = 4
(n+1)/2 = (3+1)/2 = 2nd score
Example: 1, 3, 5, 7
Median = average of 2nd and 3rd scores = 4
Mode
Mode: Most common score
Example: 1, 3, 3, 4, 5, 7
Mode = 3 (only score that occurs twice)
Mode
Mode: Most common score
Example: 1, 3, 3, 4, 5, 7
Mode = 3 (only score that occurs twice)
Questions
Four students in a psychology class received
scores of 2, 3, 3, and 4
What is the mean?
What is the median?
What is the mode?
Questions
Four students in a psychology class received
scores of 2, 3, 3, and 4
What is the mean?
3
What is the median?
What is the mode?
(2+3+3+4)/4
Questions
Four students in a psychology class received
scores of 2, 3, 3, and 4
What is the mean?
3
What is the median? 3
What is the mode?
(2+3+3+4)/4
average of 3 and 3
Questions
Four students in a psychology class received
scores of 2, 3, 3, and 4
What is the mean?
3
What is the median? 3
What is the mode?
3
(2+3+3+4)/4
average of 3 and 3
most common score
Questions
For which of the following distributions of scores
would the median most clearly be a more
appropriate measure of central tendency than the
mean?
A.
B.
C.
D.
16, 28, 4, 8, 24
9, 6, 9, 12, 9
5, 19, 4, 5, 2
8, 9, 12, 10, 16
Questions
For which of the following distributions of scores
would the median most clearly be a more
appropriate measure of central tendency than the
mean?
A.
B.
C.
D.
16, 28, 4, 8, 24
9, 6, 9, 12, 9
5, 19, 4, 5, 2 X
8, 9, 12, 10, 16
(19 is an outlier, and skews the mean)
Measures of Variation
A measure of variation tells us how similar or
diverse the scores are (e.g. how packed together
or dispersed the scores are)
• Range = Difference between highest and lowest scores
• Variance = Average of squared difference from mean
• Standard deviation = Square root of variance
Measures of Variation
A measure of variation tells us how similar or
diverse the scores are (e.g. how packed together
or dispersed the scores are)
• Range = Difference between highest and lowest scores
• Variance = Average of squared difference from mean
• Standard deviation = Square root of variance
Measures of Variation
A measure of variation tells us how similar or
diverse the scores are (e.g. how packed together
or dispersed the scores are)
• Range = Difference between highest and lowest scores
• Variance = Average of squared difference from mean
• Standard deviation = Square root of variance
Measures of Variation
A measure of variation tells us how similar or
diverse the scores are (e.g. how packed together
or dispersed the scores are)
• Range = Difference between highest and lowest scores
• Variance = Average of squared difference from mean
• Standard deviation = Square root of variance
Range
Range: difference between highest and lowest
scores
Example: 1, 4, 7
Range = 7-1 = 6
Range
Range: difference between highest and lowest
scores
Example: 1, 4, 7
Range = 7-1 = 6
Variance
Variance: Average of squared difference from
mean
Example: 2, 5, 8 (average = 5)
Variance = 6
average of (2-5)2, (5-5)2, and (8-5)2
average of 9 , 0 , and 9
Variance
Variance: Average of squared difference from
mean
Example: 2, 5, 8 (average = 5)
Variance = 6
average of (2-5)2, (5-5)2, and (8-5)2
average of 9 , 0 , and 9
Standard Deviation
Standard Deviation: square root of variance
Example: Variance = 9
Standard Deviation = 3
Standard Deviation
Standard Deviation: square root of variance
Example: Variance = 9
Standard Deviation = 3
Questions
Which of the following would be the BEST
choice to measure variability?
A.
B.
C.
D.
Standard deviation
Mode
Range
Mean
Questions
Which of the following would be the BEST
choice to measure variability?
A.
B.
C.
D.
Standard deviation
Mode
Range
Mean
X
Questions
Four students in a psychology class received
scores of 2, 3, 3, and 4
What is the range?
What is the variance?
Questions
Four students in a psychology class received
scores of 2, 3, 3, and 4
What is the range? 2 (4-2)
What is the variance?
Questions
Four students in a psychology class received
scores of 2, 3, 3, and 4
What is the range? 2 (4-2)
What is the variance? 0.5 (average of 1, 0, 0, and
1)
Normal Distribution & Empirical Rule
Normal Distribution (“Bell Curve”): Commonly
occurring distribution
Empirical Rule:
• 68% of population within 1 standard deviation (+/- 1s)
• 95% within 2s
• 99.7% within 3s
Questions
The average IQ is 100, and the standard deviation is
15
Q: Assuming a normal distribution, approximately
what percentage of individuals have an IQ of more
than 115?
A: 16%
50% of individuals score below average, and 34% (half of
68%) of individuals score between 100 & 115
Questions
The average IQ is 100, and the standard deviation is
15
Q: Assuming a normal distribution, approximately
what percentage of individuals have an IQ of more
than 115?
A: 16%
50% of individuals score below average, and 34% (half of
68%) of individuals score between 100 & 115
Skewed Distribution Curves
Questions
If a curve is positively skewed…
Is the mean, median or mode furthest to the
right?
Which is furthest to the left?& 115
Questions
If a curve is positively skewed…
Is the mean, median or mode furthest to the
right? mean, because it is skewed the most by outliers
Which is furthest to the left? the mode (the median
is always in the middle)
Questions
If a curve is positively skewed…
Is the mean, median or mode furthest to the
right? mean, because it is skewed the most by outliers
Which is furthest to the left? the mode (the median
is always in the middle)
Questions
If a curve is positively skewed…
Is the mean, median or mode furthest to the
right? mean, because it is skewed the most by outliers
Which is furthest to the left? the mode (the median
is always in the middle)