Distributions and Graphical Representations

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Distributions and Graphical Representations
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Statistics

• the science of collecting, analyzing, and drawing
  conclusions from data

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Descriptive statistics

• the methods of organizing summarizing data

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Inferential statistics

• involves making generalizations from a sample to
  a population

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Population

• The entire collection of individuals or objects
  about which information is desired

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Sample

• A subset of the population, selected for study in
  some prescribed manner

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Variable

• any characteristic whose value may change from
  one individual to another

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Data

• observations on single variable or simultaneously
  on two or more variables

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Types of Variables
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Categorical variables

• or qualitative
• identifies basic differentiating characteristics
  of the population

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Numerical variables

• or quantitative
• observations or measurements take on numerical
  values
• makes sense to average these values
• two types - discrete continuous

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Discrete (numerical)

• listable set of values
• usually counts of items

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Continuous (numerical)

• data can take on any values in the domain of the
  variable
• usually measurements of something

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Classification by the number of variables

• Univariate - data that describes a single
  characteristic of the population
• Bivariate - data that describes two
  characteristics of the population
• Multivariate - data that describes more than two
  characteristics (beyond the scope of this course

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Identify the following

• gender
• age
• hair color
• smoker
• systolic blood pressure
• number of girls in class

• categorical
• numerical
• categorical
• categorical
• numerical
• numerical

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Types of Distributions

• 4 common types

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Symmetrical

• refers to data in which both sides are (more or
  less) the same when the graph is folded
  vertically down the middle
• bell-shaped is a special type
• has a center mound with two sloping tails

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Uniform

• refers to data in which every class has equal or
  approximately equal frequency

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Skewed (left or right)

• refers to data in which one side (tail) is longer
  than the other side
• the direction of skewness is on the side of the
  longer tail

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Bimodal (multi-modal)

• refers to data in which two (or more) classes
  have the largest frequency are separated by at
  least one other class

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How to describe a graph

• Dotplots
• Stem leaf plots
• Histograms
• Boxplots

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1. Shape - Type of distribution

• refers to the overall shape of the distribution
• symmetrical, uniform, skewed, or bimodal

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2. Center

• discuss where the middle of the data falls
• three types of central tendency
• mean, median, mode

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3. Spread

• discuss how spread out the data is
• refers to the variability of the data
• Range, standard deviation, IQR

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4. Unusual occurrences

• outliers - value that lies away from the rest of
  the data
• gaps
• clusters
• anything else unusual

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5. In context

• You must write your answer in reference to the
  specifics in the problem, using correct
  statistical vocabulary and using complete
  sentences!