Frequency Distribution
How tabular and graphical methods used for categorical data. summary of data that shows number of items in each of several nonoverlapping classes. For example, data from a sample of 50 soft drink purchases would be organized in this way.
Relative and Percent Frequency Distribution
measures proportion or percentage of items in each class. Fraction or proportion of items belonging to a class. Frequency of the class/n (total observations). Percent Frequency is the result X 100.
Bar Chart
used to display categorical data summarized in frequency, relative, or percent. X axis is labels used for categories, y is type of frequency.
Pie Chart
graphical way to show categorical data. only relative or percent frequencies. circle represents all the data. 360 degrees so if relative frequency of .38 to determine how much of circle should be shaded, multiply 360(.38)=136.8 degrees should be shaded in
Width:
found by: (largest data value- Smallest Value)/# of classes. Round number of classes up if decimal answer. Class and width not independent, # classes and width mainly trial and error.
Class Limits:
chosen so that each data item belongs to one class only. Necessary to determine where each value belongs, not needed for categorical data because each data item naturally fell into a separate class.
Class midpoint
Class midpoint: value halfway between the lower and upper class limits.
Dot Plot
useful for comparing distribution of the data for two or more variables. horizontal axis shows range for the data. each data value represented by dot placed above axis, which are stacked vertically when more then one frequency exists.
Histogram
information on shape or form of a distribution. used to display the different types of frequency distributions. Variable of interest on horizontal axis and frequency on vertical axis. No natural separation between rectangles of adjacent classes which help
Skewed Left
tail extends farther to the left
Skewed Right
Tail extends farther to the right
ex. Data housing prices, salaries, purchase amounts...
Symmetric Skewed
Left tail mirrors right tail roughly
Cumulative Frequency Distribution
Cumulative Frequency Distribution: for quantitative data, uses the number of classes, class widths, and class limits and shows the number of data items with values less than or equal to the upper class limit of each class.
Ogive
graph of cumulative distribution. data values on horizontal axis, cumulative frequencies on vertical axis. Constructed by plotting point corresponding to cumulative frequency of each class. So that no gaps between classes, 14.5 is plotted instead of 14 bu
Stem-Leaf Display
can be used to show both rank order and shape of a data set simultaneously. First arrange leading digits of each data value to left of a vertical line. Right side of data have the last digit of the number. Digit(s) on left of vertical line form the stem,
Exploratory Data Analysis
Simple arithmetic and easy-to-draw graphs that can be used to summarize data quickly.
Crosstabulations and Scatter Diagrams use
will assist in the understanding of the relationship between two variables
Crosstabulation
Tabular summary for two variables. Can combine categorical and quantitative variables, but also can combine two of same types. Ex: Quality rating categorical, goes on left with Total at the bottom. And across top will be the classes of meal prices. With t
Simpson's Paradox
some cases where conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the unaggregated data. Before drawing any conclusions about relationship between two variables show for crosstabulation involving aggregated da