Section 1.1 and 1.2

Cases:

• The objects described by a set of data

• They can be customers, companies, subjects in a study,
  units in an experiment, or other objects.

Variable:

• is a special characteristic of a case

Values:

• Different cases can have different values of a variable

Label:

• is a special variable used in some data sets to
  distinguish among the different cases

Categorical Variable:

• places each case into one of several groups, or categories

Quantitative Variable:

• takes numerical values for which arithmetic operations such as adding and averaging make sense

Key Characteristics of a Data Set:

Every data set is accompanied by important background
information. In a statistical study, always ask the following
questions:

• Who? What cases do the data describe? How many
  cases does a data set have?

• What? How many variables does the data set have? What
  are the exact definitions of these variables? What are the
  units of measurement for each quantitative variable?

• Why? What purpose do the data have? Do the data
  contain the information needed to answer the questions of
  interest?

Exploratory Data Analysis:

• Begin by examining each variable by itself. Then, move
  on to study the relationships among the variables

• Begin with a graph or graphs. Then, add numerical
  summaries of specific aspects of the data.

Variables:

• We construct a set of data by first deciding which cases or units we want to study. For each case, we record information about characteristics that we call variables

• Characteristics of the individual

Distribution of a Variable:

• To examine a single variable, we graphically display its distribution

• The distribution of a variable tells us what values it takes and how often it takes these values

• Distributions can be displayed using a variety of graphical tools. The proper choice of graph depends on the nature of the variable

• Categorical Variable:

  • Pie chart

  • Bar Graph

• Quantitative Variable:

  • Histogram

  • Stemplot

The Distribution of a Categorical Variable:

• list the categories and gives the count of the percentage of individuals who fall into each category

• Pie charts: show the distribution of a categorical variable as a “pie”. Its slices’ sies reflect the counts or percent’s for the categories

• Bar graph: represent categories as bars whose heights show the category counts or percent’s

The Distribution of a Quantitative Variable:

• The distribution of a quantitative variable tells us what values the variable takes on and how often it takes those values

• Stemplots: separate each observation into a stem and a leaf that are then plotted to display the distribution while maintaining the original values of the variable

• Histograms: show the distribution of a quantitative variable by
  using bars. The height of a bar represents the number of
  individuals whose values fall within the corresponding class

To Construct Stemplots:

1.) Separate each observation into a stem (all but the rightmost digit)
and a leaf (the remaining digit)

2.) Write the stems in a vertical column; draw a vertical line to the right
of the stems

3.) Write each leaf in the row to the right of its stem; order the leaves,
if desired

4.) If there are very few stems (when the data cover only a very small range
of values), then you might want to create more stems by splitting the
original stems

Examining Distributions:

• In any graph of data, look for the overall pattern and for striking deviations from that pattern

• You can describe the overall pattern by its shape, center, and
  spread

• An important kind of deviation is an outlier, an individual that falls
  outside the overall pattern

• Extreme values of a distribution are in a tail of the distribution

• A peak in a distribution is called a mode. Bimodal Distribution

• A distribution is symmetric if the right and left sides of the graph are approximately mirror images of each other

• A distribution is skewed to the right (right-skewed) if the right side of the graph (containing the half of the observations with larger values) is much longer than the left side

• It is skewed to the left (left-skewed) if the left side of the graph is
  much longer than the right side

Outliers:

• An important kind of deviation is an outlier

• Outliers are observations that lie outside the overall pattern of a distribution

• Always look for outliers and try to explain them

Time Plots:

• A time plot shows behavior over time

• Time is always on the horizontal axis, and the variable being measured is on the vertical axis

• Look for an overall pattern (trend) and deviations from this trend. Connecting the data points by lines may emphasize this trend

• Look for patterns that repeat at known regular intervals (seasonal variations)