Handout 1

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Handout 1

• Describing Data

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Summarizing and Describing Data (Graphical)

• Pareto Chart
• Histogram

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Pareto Chart

• Consider a company that sells business bags.
  Among these bags, some items generate more
  revenues than other items. By ranking the items
  according to the revenue, the company will know
  which items they have to emphasize (in terms of
  cost management, etc). For such a purpose, a
  Pareto chart is useful.

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Pareto Chart Example
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Pareto Chart Example
The following data is on our IM Folder. Open the
excel file Bag sales
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A Procedure to make a Pareto

• Compute the revenue for each item
• Compute the total revenue
• Sort the data according to the revenue
• Compute the percentage of revenue for each item
• Compute the cumulative percentage of revenue
• Make the Pareto Chart

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Pareto Chart Example
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From the Pareto Chart example, we can learn

• Business bags black, Business bag brown, and OA
  bags count above 70 of total revenue.
• Require a lot of inventory
• Too much reliance on a small number of items.
  Need more marketing effort for suit cases and
  name card folders.

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Pareto Chart Example 2Visualizing Revenue by
Clients

• Use Pivot Table
• Pareto Chart

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Example (Sales by Clients spread sheet)
This data is a part of Sales by clients data
stored on our Applied Stat Folder. From this
data, we would like to make (1) a table that
ranks the revenue by clients, and (2) Pareto Chart
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Revenue Ranking Table (Example of the Use of
Pivot Table)
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Pareto Chart Example 2
100
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Histogram and frequency table

• Example
• Visualizing your clients age range using
  histogram.

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Histogram Example
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From the histogram, we can learn that

• Clients of age between 35 and 45 are the primary
  clients.
• It is important to maintain the satisfaction
  of these clients.
• Provide new services for other age ranges to
  increase client base.

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Making Histogram and Frequency Table

• Open the data Clients list which is stored in
  our Applied Stat Folder. This is the data for the
  histogram shown in the previous slides.

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Numerical Measure of data summary (I)

• Difference between Population and Sample
• Mean (Average)
• Median

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Difference between Population and Sample

• Population
• A population is the complete set of all items in
  which an investigator is interested.

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Examples of Populations

• Names of all registered voters in the United
  States.
• Incomes of all families living in Daytona Beach.
• Grade point averages of all the students in your
  university.

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• A major objective of statistics is to make an
  inference about the population. For example What
  is the average income of all families living in
  Daytona Beach.
• Often, collecting the data for the population is
  costly or impossible. Therefore, we often collect
  data for only a part of the population. Such data
  is called a Sample.

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A Sample

• Sample
• A sample is an observed subset of population
  values.

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Numerical Measure of Summarizing Data 1-1 Mean
(Average)

• How to compute the mean (average)
• Understanding the mathematical notation of the
  mean (average)
• Cautionary notes for the use of the mean

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1-2 How to compute the mean

• Sum all the data, then divide it by the number of
  observations.
• We use the term sample size to mean the number
  of observation.

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1-3 Computing the mean an example

• This is a sample data of the ages of your
  business clients. Compute the mean age of your
  clients in this sample.
• Note that this is a typical data format that we
  will encounter in this course. It has the
  observation id (Client ID), and the value of the
  variable of interest (age) for each observation.

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2-1 Understanding the mathematical notation of
the mean
This is one of the most common format of data
that we deal with. In the first column, we have
the observation id, and the second column has the
value for each observation. (Often observation id
is omitted) In the previous example, variable X
is the age of the clients. Then observation id 1
means that this is the first customer in your
customer list, and x1 is the age of the customer.
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2-2 Understanding the mathematical notation of
the mean
When a data set is given in this format, the
sample mean of the variable X, denoted by ,is
given by
The notation, is the summation
notation. This is simply the sum from x1 to xn
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2-3 Sample Mean and Population Mean

• Most often we use a sample data. For example, if
  we want to know the popularity rating of the
  current government, we may use data from 10,000
  interviews. This is just a part of the whole
  voting population.
• Though not often, we may have the data from the
  whole population.

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2-4 Sample Mean and Population Mean

• Later, it will become convenient to distinguish
  Sample mean and population mean. Thus we will use
  different notation for the sample mean and the
  population mean.

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2-5 Notations for the sample mean and the
population mean
For a sample mean, we use the following notation
For the population mean, we use µ to denote the
population mean. We also use upper case N to
denote the sample size.
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3-1 Cautionary note

• Mean (average) is not necessarily the center
  of the data

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3-2 Example

• The average Japanese household saving in year
  2005 is ?17,280,000
• This data may make you feel well, if I do not
  have this much saving, I am not normal
• Now, take a look at the histogram of the
  household saving in the next slide.

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The mean may not be the center of the data. An
example
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• One may think that the average is the normal
  household. However, you can see that a lot of
  households have savings much less than the
  average. The average saving is very high because
  a few households have huge savings.
• In such case, median can give you a better
  sense of a normal household. The definition of
  the median is given in the next slide.

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4-1 Median

• Sort the data in an ascending order. Then the
  median is the value in the middle (middle
  observation)

When the number of observation is an even number,
then there is no middle observation. In such
case, take the average of the two middle numbers
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4-2 Median Exercise

• Open the file Computation of median A. This
  data contains the age of a companys clients.
  Find the median age of this sample
• Open the file Computation of median B. This
  data contains the revenue of bag sales. Find the
  median of this sample.

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Japanese Household saving revisited
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Corresponding chapters

• This lecture note covers the following topics of
  the textbook.
• 1.1 Sampling
• Example 2.6 Pareto Diagram
• 2.4 Arithmetic Mean, Median