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Definitions
Intro to Statistics and
Frequency Distributions
Finite Mathematics
Section 10.1
Definitions, Continued
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Population vs. Sample:
A population
includes all objects of interest whereas a sample is
only a portion of the population.
Parameters are associated with populations and
statistics with samples
samples. Parameters are usually
denoted using Greek letters (µ and σ) while
statistics are usually denoted using Roman letters
(x, s). Usually, we compute statistics, and use
them to estimate parameters.
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Statistics: A collection of methods for planning
experiments; obtaining data; organizing,
summarizing, presenting, analyzing, and
interpreting the data; and drawing conclusions.
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Descriptive Statistics: The collection,
collection
organization, analysis, summarization, and
presentation of data.
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Inferential Statistics: Generalizing from samples
to populations using probabilities; performing
hypothesis testing, determining relationships
between variables, and making predictions.
More Definitions
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Raw Data:Data collected in original form.
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Classes / class intervals:
Subgroups within a
set of collected data. In general, a data set is
divided into between 5 and 15 class intervals, each
containing at least one data value.
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Frequency:
The number of times a certain
value or class of values occurs.
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Frequency Distribution Table: The organization of
raw data into table form using classes and
frequencies. Our text uses the convention that
each class interval contains its left endpoint but
not its right endpoint.
Observations: Numerical quantities that measure
specific characteristics. Examples include height,
weight, gross sales, net profit, etc.
And More Definitions
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Relative Frequency of a class is computed by
dividing the frequency of that class by the total of
all frequencies.The relative frequency is the same
as the empirical probability that an individual data
value will fall within that class.
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Cumulative Frequency
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y of a class is the sum of the
frequency of that class and the frequencies of all
the preceding classes which are listed in some
sensible order (numerical order, alphabetical
order, etc.)
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Cumulative Relative Frequency of a class is the
sum of the relative frequency of that class and the
relative frequencies of all of the preceding classes
which are listed in some sensible order.
Histogram
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A histogram displays data by using
adjacent vertical bars of various heights to
represent frequencies. A frequency
histogram shows how often the collected
data fall within a given class
class, while a
relative frequency histogram tells the
percentage of the sample that falls into that
class. If each bar in a relative frequency
histogram is constructed with a width of
one, then the area of the bar is the same as
the estimated probability associated with it.
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Frequency Distribution Table
Example
A clerk at the Carnegie Library counted the number of books checked
out by individual patrons between 10 and 10:30 a.m. on Saturday
August 24. During this time interval, thirty-three individuals checked
out books. The number of books checked out by individual patrons
were:
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10 11 11
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11 11 11 11 12 13 14 14 14 15 16
Use
this data to create a frequency table containing frequency,
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relative frequency, and cumulative frequency. Then create a
frequency histogram, a relative frequency histogram, and a
cumulative frequency histogram
Frequency Histogram
Cumulative Frequency Histogram
Relative Frequency Histogram
Normal Probability Distribution
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Skewed Distributions
Distribution skewed to
the right.
Distribution skewed to
the left.
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