AP Statistics Introduction

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AP StatisticsIntroduction Chapter
1.1Variables, Distributions Graphs

• Goals What will we know and be able to do as a
  result of todays Lesson?

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You will be able to know, explain and use the
following vocabulary

• Individual
• Variable
• Categorical Variable
• Quantitative Variable
• Distribution
• Exploratory Data Analysis

• Count
• Percent
• Bar Graph
• Pie Chart
• Dotplot
• Stemplot
• Center, Spread, Shape
• Outlier

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Here are some definitions

• Individual Objects described by a set of data.
  They may be people, animals, things, etc.
• Variable Any characteristic of an individual.
  The variable will likely take on different values
  for different individuals.
• (Can you think of some more examples?)

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more definitions

• Categorical Variable A variable which focuses
  on a characteristic of an individual, allowing it
  to be placed into one of several groups or
  categories.
• Quantitative Variable A variable which focuses
  on a characteristic of an individual that takes
  on numerical values for which arithmetic
  operations can be performed.
• (Can you think of some more examples?)

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more definitions

• Distribution a way of demonstrating what values
  a variable take on and how often it takes each
  value.
• Exploratory Data Analysis Using statistical
  tools to examine data and describe its main
  features. Comparing variables, providing graphs
  and doing numerical summaries are specific
  strategies.

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more definitions

• Count The number of observations that fall into
  a particular category, when analyzing individuals
  with a categorical variable.
• Percent The percentage of observations that
  fall into a particular category, when analyzing
  individuals with a categorical variable. This is
  found by dividing the count by the total number
  of observations.

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more definitions

• Bar Graph A graph which is fashioned by
  separate rectangular bars, whose heights
  represent either the count or the percentage of
  individuals within each category.

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more definitions

• Pie Chart A circle graph which represents each
  category percentage by a number of degrees out of
  360.

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One kind of Quantitative Display

• Dotplot A simple way to represent a summary of
  quantitative data. Create an x-axis with the
  quantitative values upon it. Place a dot over
  each value as it is represented in the data.
• See the example done in class for soccer goals

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more definitions

• Looking for an overall PATTERN?
• Center What value seems to divide the data
  into two parts - half of which are higher, and
  half of which are lower?
• Spread What are the largest and smallest
  values?
• Shape Do the data form a symmetric mound? Is
  the distribution flat? Does it have a tail?
  to the left? or to the right?
• Outlier Do any individual observations fall
  outside the overall pattern of a graph?

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Another type of Quantitative Display

• Stemplot A more complicated way to represent a
  summary of quantitative data, especially when
  the spread of the data is very large.
• Separate each observation in two parts, a stem
  and a leaf (as demonstrated in class).
• Write the stems vertically in increasing order.
• Draw a vertical line to the right of the stems.
• Go though the data, writing down the leaves to
  the right of each stem.
• Rewrite the leaves in increasing order.
• Provide a key for what each stem/leaf means.
• See the example done in class for Caffeine
  content

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A Variation on the Theme

• Split Stemplot Allow the 2 stems of the same
  value to represent an upper and lower half of the
  leaves.
• Tips Make sure you always have the same number
  of leaves allotted to each stem when splitting
  stems
• Five stems is a good minimum
• Too many stems will flatten the graph
• Too few will create a skyscraper shape
• You achieve greater flexibility by rounding the
  data first.
• See the example done in class for Caffeine
  content

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Whats on for tomorrow??

• The remainder of Section 1.1 Histograms and
  your TI-83