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Chapter 3
Chapter 3
Data Description
Data Description
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Outline
Outline
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Introduction
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Measures of Central Tendency
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Measures of Variation
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Measures of Position
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Objectives
Objectives
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Summarize data using the measures
of central tendency
, such as the
mean, median, mode.
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Describe data using the measures of
variation
, such as the
range
,
standard
deviation
and
coefficient of variation.
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Identify the position of a data value
in a data set using various
measures of position, such as
percentiles, quartiles
and
zscores
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Measures of Central Tendency
Measures of Central Tendency
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A
statistic
statistic
is a characteristic or
measure obtained by using the data
values from a sample
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A
parameter
parameter
is a characteristic or
measure obtained by using the data
values from a specific population
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The Mean (arithmetic average)
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The
mean
mean
is defined to be the sum of
the data values divided by the total
number of values
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The mean, in most cases, is not an
actual data value
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We will compute two means: one for
the sample and one for a finite
population of values
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The Sample Mean
The Sample Mean
n
X
n
X
X
X
X
n
∑
=
+
+
+
...
=
2
1
X
The symbol
represents the sample mean.
is read as “Xbar”.
The Greek symbol
is read as “sigma”
and it means “to sum”
X
The Sample Mean The Sample Mean ExampleExampleweeksnXXThe ages in weeks of a random sample of six kittens at an animal shelter are 3, 8, 5, 12,14 and 12Find the average age of this sampleThe Population MeanThe Population Mean
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93121220,000$=59,000+9,000+12,000+20,000+50,000==NX∑μA small company consists of the owner, the manager, the salesperson, and two technicians. The salaries are listed as $50,000, $20,000, $12,000, $9,000 and $9,000 respectively (Assume this is the population)Then the population mean will be:10MDMDThe Median The Median Example Example circle5The weights (in pounds) of seven soldiers are 180, 201, 220, 191, 219, 209, and 186. Find the mediancircle5Arrange the data in order and select the middle point
The Population Mean

Example
Example 
The Median
The Median
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When a data set is ordered, it is
called a
data array
data array
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The
median
median
is defined to be the
midpoint of the data array
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The symbol used to denote the
median is
12
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The Median
The Median
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In the previous example, there was
an
odd number
odd number
of values in the
data set
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In this case it is easy to select the
middle number in the data array
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The Median
The Median
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When there is an
even number
even number
of
values in the data set, the median
is obtained by taking the
average
average
of the two middle numbers
of the two middle numbers