Discussion of topics from Sections 1.1 1.3

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Discussion of topics from Sections 1.1 1.3
The significance of the Median and Mean.
The median divides a set of single variable data
into two equal halves.
How can we use the median to possibly set some
priorities?
If the median age in a large urban housing
project is 17, then half the population is 17 or
under. So issues like day care, recreation, and
schools are important to residents and should be
priority items to management.
If the median age is 55, then issues such as
convenient health care and wheel chair
accessibility should be residents concerns as
well as managements.
Source Kime, Chapter 1
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The median is (relatively) unchanged by changes
above and below it.
For example, as long as the median income is
larger than the poverty level, it will remain the
same even if all poor people suddenly increase
their incomes up to that level and everyone
elses income remains the same.
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The mean is the average value of one variable
data.
The mean is the most commonly cited statistic in
the news media.
An advantage of the mean is that it can be used
for calculations relating to the whole data set.
(It is also easy to compute.)
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Suppose a corporation wants to open a new factory
similar to its other factories. If the managers
know the mean cost of wages and benefits for
employees, they can make an estimate of what it
will cost to employ the number of workers needed
to run the new factory.
Total employee cost (mean cost for employees)
( of employees)
The mean, unlike the median, can be affected by a
few extreme values (called outliers).
For example, suppose Bill Gates, founder of
Microsoft and a very wealthy man, were to move
into a town of 10,000 people, all of whom earned
nothing.
What is the median income of the town?
Whats the mean income of the town?
Gates is worth about 56 billion 56109 so the
mean would be about 56105 5.6 million.
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HEADLINE Million-dollar Manhattan apartment? Ju
st about average
According to a report cited on money.cnn.com in
2006 the median price of purchasing an apartment
in Manhattan was 880,000 and the mean price was
1.4 million.
How could there be such a difference in price?
Which value do you think better represents
apartment prices in Manhattan?
Comment If you are shopping for an apartment in
Manhattan the median price is probably more
important since half the apartments cost 880,000
or less.
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Exercise You have the following data

• Compute the mean.
• Compute the median.

55.14
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c) Change one of the entries in the table so that
the median stays the same but the mean increases.
d) Adjoin a value to the table so that the median
stays the same.
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Exercise Suppose that annual salaries in a
certain corporation are as follows.

• Find the mean annual salary.
• b) Find the median annual salary.

24,700
18,000
c) Suppose that an advertisement is placed in the
newspaper giving the average salary of employees
as a way to attract applicants. Whats your
opinion of this ad?
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Graphical representation of data.
When you encounter a graph in an article or you
produce one for your job, there are three
elements that should always be present

• An informative title that succinctly describes
  the graph.
  
• Clearly labeled axes (or a legend) including the
  units of measurement.
  
• The source of the data cited in the data table,
  in the text, or on the graph.

Ill try to provide these in displays!
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A nice Example
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Exercise Below is a scatter plot of the median
age of the U.S. population, 1850 2050. (Beyond
2005 the values are projections.)
This particular type of graph is called a time
series because it shows changes over time.
In newspapers and magazines, the time series is
the most frequently used form of data graphic.
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• Describe how the median age of the U.S.
  population changed from 1850 to 1950.
  
• Over the entire time period indicated in the
  graph what implication can you draw about the
  U.S. population. Explain your reasoning.

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Example A 60-Second Summary
The annual federal surplus () or deficit (-)
since World War II is shown in the line graph
which is a time series. Construct a 60-second
summary describing the changes over time.
Give a topic sentence that describes the graph
as a whole.
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Sample topic sentence Between 1945 and 2005
the annual U.S. federal deficit moved from a
30-year stable period, with as little as 0
deficit, to a period of oscillation, leading in
2005 to the largest deficit ever recorded.
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Exercise The following three graphs describe two
cars A and B.
Answer the following True/False and explain your
reasoning.

• The newer car is more expensive.
• The slower car is larger.
• The larger car is newer.
• The less expensive car carries more passengers.