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1.1 Displaying Distributions with Graphs
Individuals
 are the objects described by a set of data. Individuals may be people, but they may also be business firms, common stocks,
or other objects.
Variable
 any characteristic of an individual
Categorical
variable
 places an individual into one of several groups or categories
Quantitative
variable
 takes numerical values for which arithmetic operations such as adding and averaging make sense.
Distribution
 tells what values it takes and how it takes and how often it takes these values
Pareto
chart
 bar graph whose categories are ordered from most frequent to least frequent
Outlier
 an individual value that falls outside the overall pattern
Time
plot
 variable plots each observation against the time at which it was measured
Seasonal
Variation
 a pattern in a time series that repeats itself at known regular intervals of time
Exploratory
Data
Analysis
 uses graphs and numerical summaries to describe the variable in a data set and the relations among them
1.2 Describing Distributions with Numbers
Mean
(x) average
Median
 (M) midpoint of a distribution
Five
number
summary
 median, the quartiles, max, and min
Box
plots
 based on the five number summary, useful for comparing several distributions
Variance
and
Standard
Deviation
 common measures of the spread about the mean as the center; standard deviation is zero when there I
no spread and gets larger as the spread increases
1.3 The Normal Distributions
Density
Curve
 is always on or above the horizontal axis and has exactly an area of 1 underneath it. It describes the overall pattern of a
distribution. The mean and median are equal for symmetric density curves. The mean of a skewed curve is located farther toward the long
tail than is the median
The
68

95

99
.7 rule 68% of the observations fall within standard deviation of the mean, 95% of the observations fall within 2*standard
deviation of the mean, 99.7% of the observations fall within 3*standard deviation of the mean
Standardized
Value
 z score = (X mean)/standard deviation
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This note was uploaded on 06/24/2011 for the course STA 309 taught by Professor Gemberling during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Gemberling
 Statistics

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