# Thinking Mathematically by Robert Blitzer

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```							  Thinking
Mathematically
Statistics:
12.1 Sampling, Frequency Distributions, and Graphs
Statistics
Statistics is the science of data. This involves
collecting, organizing, analyzing, and
interpreting numerical information, as well
as drawing conclusions based on the data.
Types of Statistics
• Descriptive Statistics utilizes   • Inferential Statistics utilizes
numerical and graphical             sample data to make
methods to look for patterns        estimates, decisions,
in a data set, to summarize         predictions, or other
the information revealed in a       generalizations about a
data set, and to present that       larger set of data.
information in a convenient
form.
Populations and Samples
• A population is the set containing all the objects
whose properties are to be analyzed
• A sample is a subset of the population.
• A random sample is a sample obtained in such a
way that every element in the population has an
equal chance of being selected for the sample.
Exercise Set 12.1 #1 (from text)
Frequency Distribution
• Collected data presented in a two column table.
The first column list the data values, the second
column the number of times each value occurs.
Exercise Set 12.1 #7
A random sample of 30 college students is selected. Each
student is asked how much time s/he spent on homework
during the previous week. The following times are obtained:
16, 24, 18, 21, 18, 16, 18, 17, 15, 21, 19, 17,
17, 16, 19, 18, 15, 15, 20, 17, 15, 17, 24, 19,
16, 20, 16, 19, 18, 17.
Construct a frequency distribution for the data.
Grouped Frequency Distribution
• Data is organized in to groups or classes.
• The minimum value for a class if the lower class
limit, the maximum is the upper class limit.
• The difference between the lower class limit and
the upper class limit is the class width and is the
same for all classes.
• The grouped frequency distribution lists the
number of data points in each class.
Exercise Set 12.1 #17
Construct a grouped frequency distribution for the age at which U.S.
presidents were inaugurated (see text)
Histograms and Frequency Polygon
• In a histogram the vertical axis gives the
frequency (or proportion) for each class of data
(the horizontal axis).
• Like the histogram, the axis of a frequency
polygon represent data class (horizontal) and
frequency for that class (vertical). In the
frequency polygon this data points are connected
by line segments.
Construct a histogram and a frequency polygon for the
data in exercise 17.
Stem-and-Leaf Display
• Data is ordered and grouped
– Grouping is often by highest digit
• Left column is the ‘group number’
• Individual of the group are listed in right column
Construct a stem and leaf plot for the data in
exercise 17.
Thinking
Mathematically
Statistics:
12.1 Sampling, Frequency Distributions, and Graphs

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