Download Statistics - Cardinal O'Hara High School

Statistics
Chapter 1:
Exploring Data
1.1 Displaying Distributions with Graphs
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Individuals
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Objects that are described by a set of data
Variables
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Any characteristic of an individual
Types of variables
• Categorical variables
• Record which of several groups or categories to which
an individual belong
• Quantitative variables
• Take numerical values on which arithmetical operations
can be performed
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Distribution of variable: values are
taken by the variable and the frequency
of the values
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Charts representing data
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Bar chart
Pie chart
Dot plot
Histogram
Stemplots
timeplots
Distributions
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Description of overall pattern:
center??
 spread??
 shape??
 symmetry??
 outliers??
 skewed??
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1.2 Describing Distributions with Numbers
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Measuring Center
The MEAN x
 The MEDIAN
 The MODE
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Measuring Spread or Variability
Quartiles
 Standard Deviation
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s
Other Measurements
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Interquartile range
IQR
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Range
Q3 – Q1
Max – Min
Q3  1.5  IQR
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Outliers
Q1  1.5  IQR
Other Measurements
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Five Number Summary:
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Minimum, Q1, Median, Q3, Maximum
Boxplot, Modified Boxplot, Side-byside boxplots
Properties of the Standard Deviation
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s measures spread by looking at how
far the observations are from their
mean.
Used when mean is chosen as the
measure of center
If there is no spread, s = 0. This
means that all observations have the
same value.
Strongly influenced by extreme values.
s2 is called variance.