Statistics 350 Notes
Final Exam Study Guide
Chapter 2
:
•
Variable –
a characteristic that differs from one individual to the next
•
Categorical variable
– places an individual into one of several groups or
categories; if it has ordered categories, it is called an
ordinal variable
(seat
location, current smoker, soft drink size, etc.)
•
Quantitative variable
– numerical values (age, number of CDs owned,
times spent talking on cell phone, etc.)
•
Explanatory vs. response variables
– which causes the other?
•
Shapes: bellshaped, uniform, skewed, unimodal, bimodal
•
Skewed right = tail is on right, median is less than mean
•
Skewed left = tail is on left, mean is less than median
•
Location (center, average): approximate middle value
•
Spread (variability): standard deviation, range
•
Outliers
– points that are not consistent with the bulk of the data
•
Mean
– the numerical average value (mean of a sample = xbar)
•
The mean is sensitive to extreme observations
•
The median is resistant to extreme observations
•
Median = 50
th
percentile, Q
2
•
First quartile = 25
th
percentile, Q
1
•
Third quartile = 75
th
percentile, Q
3
•
Interquartile range (IQR *middle 50% of data) = Q
3
 Q
1
•
Check for outliers by using the 1.5*IQR rule (Q
3
/Q
1
– 1.5*IQR)
•
Boxplots: cannot confirm shape
Normal Distributions
•
Standard deviation
– the measure of the spread of the observations from
the mean (roughly, the average distance the observations fall from the mean)
•
Variance = s
2
, standard deviation = s
•
Interpretation of the standard deviation: The weights of small orders of
French fries are roughly 6 grams away from their mean weight of 73.6 grams,
on average.
•
Standard deviation is sensitive to outliers and extreme observations
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Empirical Rule – For bellshaped curves, approximately…
•
68% of the values fall within 1 standard deviation from the mean in either
direction
•
95% of the values fall within 2 standard deviations from the mean in either
direction
•
99.7% of the values fall within 3 standard deviations from the mean in either
direction
•
Standardized scores (zscore) – the distance between the observed value and
the mean, measured in terms of the number of standard deviations
•
Zscore = (observed value – mean) / standard deviation
Chapter 3
:
•
Selection bias
– if the method for selecting the participants produces a
sample that does not represent the population of interest
•
Nonresponse bias
– when a representative sample is chosen for a survey,
but a subset cannot be contacted or does not respond
•
Response bias
– when participants respond differently from how they truly
feel (wording of the question, the way an interviewer behaves, etc. might lead
an individual to provide false information)
•
Margin of error
– the measure of accuracy in sample surveys (how close
that proportion comes to t he truth for the entire population)
Chapter 4
•
Observational studies
– researches simply observe or question the
participants about opinions, behaviors, or outcomes
•
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 Spring '08
 Gunderson
 Statistics, Normal Distribution, Standard Deviation, researcher

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