# Thinking Mathematically Statistics

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```Thinking
Mathematically
Sampling, Frequency Distributions,
and Graphs
Statistics
Statistics is the science of data. This involves
collecting, classifying, summarizing,
organizing, analyzing, and interpreting
numerical information.
Types of Statistics
• Descriptive Statistics utilizes
numerical and graphical
methods to look for patterns
in a data set, to summarize
the information revealed in a
data set, and to present that
information in a convenient
form.
• Inferential Statistics utilizes
sample data to make
estimates, decisions,
predictions, or other
generalizations about a
larger set of data.
1
Random Samples
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.
If we want to select a random sample from a large
city to determine how the city’s citizens feel about
casino gambling we might randomly select
neighborhoods of the city and then randomly
survey people within the selected neighborhoods.
If we only select specific neighborhoods or the
first 200 people we find in the telephone directory,
then not everyone has an equal chance of being
selected.
Describing Qualitative Data
• A class is one of the categories into which
qualitative data can be classified.
• The class frequency is the number of observations
in the data set falling in a particular class.
Histogram
A histogram is like a bar graph in that the
vertical axis gives the proportion (or
relative frequency) for each interval of data
while the horizontal axis is divided into
specified intervals of equal width known as
measurement classes. However, in a
histogram, each column shares a side or
touches while in a bar graph each column is
separated.
2
Frequency Polygon
A line graph called a frequency polygon can
also be used to visually convey information.
The axes are labeled just like those in a
histogram. Once a histogram has been
constructed, put a dot at the top of each
rectangle at its midpoint. Connect each of
these midpoints with a straight line.
Finally, draw each endpoint down to touch
the horizontal axis.
3
Stem-and-Leaf Display
Two columns are created, one for the stem and one
for the leaf. The place value for the stem is
determined for the left column and the following
place value in each piece of data will be written
next to the appropriate stem in the leaf column.
As an example, if the data value is 32, the 3 may
be designated as the stem in which case the 2
would be the leaf. If the data point is 5.8, the ones
place may be the stem and the tenths place the leaf
so that the 5 would be in the stem column with the
8 next to it in the leaf column.
Thinking
Mathematically
Sampling, Frequency Distributions,
and Graphs
4
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