What is Statistics?

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What is Statistics?

• Definition of Statistics
• Statistics is the science of collecting,
  organizing, analyzing, and interpreting data in
  order to make a decision.
• Branches of Statistics
• The study of statistics has two major branches
  descriptive(exploratory) statistics and
  inferential statistics.
• Descriptive statistics is the branch of
  statistics that involves the organization,
  summarization, and display of data. In this
  course, from chapter 1 through Chapter 5, they
  are talking about Descriptive statistics.
•  Inferential statistics is the branch of
  statistics that involves using a sample to draw
  conclusions about population. A basic tool in the
  study of inferential statistics is probability.
  In this course, starting from Chapter 9, they are
  talking about inferential statistics.

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Chapter 1 Picturing Distributions with Graphs
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Chapter outline

• Individuals and variables
• Categorical variables
• Pie Charts and bar graphs
• Quantitative variables
• Histograms
• Interpreting histograms
• Quantitative variables Stemplots
• Time plots

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Examining Distributions- Introduction

• Definitions
• Individuals the objects described by a set of
  data
• Variable any characteristic of an individual

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Examples

• College student data every currently enrolled
  student date of birth, gender, major, GPA and
  so on
• Employee data every employee age, gender,
  salary, job type

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Variables

• Categorical variable categories, groups
• Quantitative variable numerical values
• Distribution of a variable what values it takes
  and how often it takes these values

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Examples

• College student data every currently enrolled
  student DOB, gender, major, GPA, and so on
• Employee data every employee age, gender,
  salary, job type
• We can see distributions easily using graphs. It
  is possible to see distributions using numbers
  which describe the data.

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Example 1.1 (Page 5)
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• Exploratory data analysis describes the main
  feature of data.
• 1. Examine each variable
• 2. Study the relationships among the variables
• 3. Start with graphs and add some numerical
• summeries.

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Categorical variables --- bar graphs and pie
charts

• Distribution of categorical variables categories
  by relevant count or percent of individuals.
• Graphs bar graph, pie chart
• Pie chart figure 1.1 (P. 7)/ must include all
  categories
• Bar graph figure 1.2 (P. 8)/height?individuals
  weight
• gaps between bars and order is not
  important.
• Note Its only for single variable now (for
  example college major, tire model, final exam
  grade).

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Pie Chart in Figure 1.1 shows us each material as
a part of the whole
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Quantitative variables histograms

• How to make histograms
• Step 1. Choose the classes. Divide the range of
  the data into classes of equal width.
• Step 2. Count the individuals in each class.
• Step 3. Draw the histogram.
• Example 1.3

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Example 1.3 (P. 11)
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Interpreting histograms

• Interpretation What do we see?
• Overall pattern and striking deviations.
• Overall pattern
• Shape, center, spread symmetric, skewed to the
  right/left, clustered.
• striking deviations
• Outlier

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Example 1.5 (P. 13)
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Example 1.6 (P. 14)
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Quantitative variables stemplots

• Another way to display a distribution of
  quantitative variables.
• How to make stemplots
• 1. Sort data in increasing order first
• 2. Separate each observation into a stem
  consisting of all but the final digit, and a
  leaf, the final digit.
• 3. Write the stems in a vertical column with the
  smallest at the top, and draw a vertical line at
  the right of this column
• 4. Write each leaf in the row to the right of its
  stem, in increasing order out from the stem.

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Quantitative variables stemplots

• Data 80, 52, 86, 94, 76, 48, 92, 69, 79, 45
• Step 1. Sort data in increasing order first
• Step 2. Decide stem
• Step 3. Fill in leaves

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Examples and Exercises

• Example 1.7 (P. 16) using Table 1.1 (P. 10)
• Example 1.8 (P. 16)

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Tips

• 1. Rounding
• 2. Splitting stems

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Quantitative variables stemplots

• For small data sets, it is quicker to make and
  presents more detailed information
• You keep data values

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Time plots

• It is for variables which are measured at
  intervals over time.
• Example 1. The cost of raw materials for a
  manufacturing process each month.
• Example 2. The price of a stock at the end of
  each day.

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Time plots

• To display change over time, make a time plot.
  Plot each observation against the time at which
  it was measured
• 1. Put time on the horizontal scale
• 2. Put the variable on the vertical scale
• 3. Connect the data points by lines
• Special case time series (for regularly measured
  variable)
• You can see 1 )seasonal variation, 2) trend

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Example 1.9 (P.18)
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Free tutoring

• The Math Assistance Complex (MAC) 122 Kell Hall
• MAC website(online tutoring available)
  www.gsu.edu/wwwclc/mathlab.htm