Ch 2 - Statistics

Data visualization

Term used to describe the use of graphical displays to summarize and present info about a data set

Frequency distribution

A frequency distribution is a tabular summary of data showing the number (frequency) of observations in each of several nonoverlapping categories or classes

Relative Frequency

Fraction or proportion of observations belonging to a class. For a data set with n observatios, the relative frequency of each class can be determined as follows

Relative frequency of a class = Frequency of the class / n

Relative Frequency Distribution

Gives a tabular summary of data showing the relative frequency of the data for each class

Percent frequency distribution

Summarizes the percent frequency of the data for each class

Bar Charts

Graphical display for depicting categorical data summarized in a frequency, relative frequency, or percent frequency distribution

Pie Chart

Presents relative frequency and percent frequency distributions for categorical data

• not best to present percentages for comparison

• Rel frequency x 360

Pareto Diagram

• In quality control, bar charts are used to identify the most important causes
  of problems.

• When the bars are arranged in descending order of height from left to right
  (with the most frequently occurring cause appearing first) the bar chart is
  called a Pareto diagram.

• This diagram is named for its founder, Vilfredo Pareto, an Italian economist.
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Dot Plot

Data represented by a dot placed above the axis

• Useful for comparing the distribution of the dat for two or more variables

Histogram

• Can be prepared for data previously summarized in either a frequency, relative frequency, or percent frequency distribution

• Place the variable of interest. on the horizontal axis and the frequency, rel frequency or percent frequency on the vertical axis

• Elinate the spaces between classes in. ahistogram for the audit time data helps show that all values between. thelwoer limit of the first class and the upper limit of the last class are possible

• Provides info of shape

  • Skewed right, Skewed left, symmetrical

Cumulative Distributions

Uses number of classes, class width, and class limits developed for the frequency distriution

• Shows the number of data items with values less than or equal to the upper class limit of each class

Cumulative relative frequency distribution

Proportion of data items

Cumulative percent frequency distribution

Percentage of data items with values less than or equal to the upper limit of each class

• Summing the relative frequencies or by dividing the cumulative frequencies by the total number of tiems

Stem-and-Leaf Display

Show simultaneously the rank order and shape of a distribution of data

• Sort the digits on each line into rank order (numbers. tothe left form the stem and digits to the right is a leaf

• Indicates which numbers have a first digit of a 6,7,8,9, etc

Crosstabulation

Summarizing Data for Two Variables Using Tables

• Method for summarizing the data for two variables

Used when:

• One variable is categorical and the other is quanittiative

• Both variables are categorical, or

• Both variables are quantitative

The left and top margin labels define the classes for the two variables

Simpson’s Paradox

The reversal of conclusions based on aggregate and unaggregaited data is called Simspon’s paradox

Data Dashboard

a Set of visual displays that organizes and presents info that is used to mointor the perfomrance of a company or organization in a manner that is easy to read

Scatter diagram

A graphical display of the relationship between two quantitative variables. ONe variable is shown on the horizontal axis and the other variable is shown on the vertical axis

Trend line

A line that provides an approximation of the relationship between two variables

Side by side bar chart

A graphical display for depicting multiple bar charts on the same displa

Stacked bar chart

Each bar is broken into rectangular segments of a different color showing the relative frequency of each class in a manner similar to a pie chart

Approximate class width

Largest data value - smallest data value/number of classes

Summarizing Categorical Data

• Frequency distr.

• Relative frequency dtr.

• Percent frequency dist.

• pie chart

• bar chart

Summarizing quantitative data

Frequency Distribution
• Relative Frequency and Percent Frequency Distributions
• Dot Plot
• Histogram
• Cumulative Distributions
• Stem-and-Leaf Display

Outliers

Medians used