Chapter 3 Outline
Introduction
What is an average?
It is a single number used to describe the central tendency of a set of data.
Examples of an average are:
The average length of the school year for students in public schools in the United States is 180 days.
The median household income for the United States was $44,389 in 2004, the most recent year for which this data
is available (
http://www.cens
us
.gov
).
The median selling price for a singlefamily home in Boston in August, 2005 was $375,000 (
The Boston Globe,
October 26, 2005
).
The mean
wage for accountants was $24.56 per hour in 2004.
(
The Census Bureau’s Income Statistics Branch
,
July,
2005
).
Computer Software Engineers’ pay averaged $38.44 per hour, while Library Technicians averaged $12.22 per
hour.
(
Bureau of Labor Statistics web site: http://stats.bls.gov, July, 2005
)
There are several types of averages.
We will consider five: the arithmetic mean, weighted mean, the median, the mode,
and the geometric mean.
Measures of Location
The purpose of a measure of location is to pinpoint the center of a set of observations.
Measure of location
: A single value that summarizes a set of data. It locates the center of the values.
The arithmetic mean, or simply the mean, is the most widely used measure of location.
Mean
: The sum of observations divided by the total number of observations.
The population mean is calculated as follows:
Population mean =
Sum of all values in the population
Number of values in the population
In terms of symbols, the formula for the mean of a population is:
Population
Mean
X
N
[
]
3
1
Where:
μ
represents the population mean. It is the Greek letter “mu.”
N
is the number of items in the population.
X
is any particular value.
indicates the operation of adding all the values. It is the Greek letter “sigma.”
X
is the sum of the
X
values.
[31] indicates the formula number from the text.
Any measurable characteristic of a population is called a
parameter
.
Paramete
r: A characteristic of a population.
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The Sample Mean
As explained in Chapter 1, we frequently select a sample from the population to find out something about a specific
characteristic of the population.
The mean of a sample and the mean of a population are computed in the same way, but the shorthand notation is different.
In terms of symbols, the formula for the mean of a sample is:
Sample
Mean
X
X
n
[
]
3
2
Where:
X
is the sample mean; it is read as “
X
bar”.
n
is the number of values in the sample.
X
is a particular value.
indicates the operation of adding all the values.
X
is the sum of the
X
values.
[32] is the formula number from the text.
The mean of a sample, or any other measure based on sample data, is called a
statistic
.
Statistic
: A characteristic of a sample.
“The mean weight of a sample of laptop computers is 6.5 pounds,” is an example
of a statistic.
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 Spring '08
 Staff
 Standard Deviation, Mean, representative, mean deviation

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