Guidelines for constructing frequency distributions and concept of independence
Steps to constructing a frequency distribution
1. Collect raw data 2. Form a data array 3. Construct a frequency distribution
Mutually exclusive classes
A data value appears in only one class
Class limits
Boundaries, there is an upper and lower limit
Classes
Categories
Pie chart
Circular display divided into segments with sizes proportional to the shares
Step 1
Data as originally collected
Histogram
Describes a frequency distribution by a series of adjacent rectangles, each with a length equal to either the absolute or relative frequency
Step 3
Divide data into classes and show the number of observations in each class
Pleasing classes
Equal widths, "right" number of classes, class widths should be round number, and if possible, no open-ended classes
Exhaustive classes
Every data value must appear in a class
Frequency polygon
From the histogram, connects the class marks by line segments, number of observations rise or fall more realistically (gradually) than for the histogram
Cumulative relative
Has classes of column 1 and frequencies of column 5
Cumulative absolute
Has the classes of column 2 and the frequencies of column 3
Cumulative frequency distributions
List number (or %) that are within or below each class
Class mark
Mid-point of each class
Open-end classes
No upper or lower limit
Step 2
Raw data is listed in either increasing or decreasing order
Frequencies
The number of something in a class
Relative frequency distribution
Useful for comparing two data arrays where the sizes of the groups are different
Absolute frequency distribution
Useful for summarizing a particular data array
Stem - and - leaf display
Uses a subset of the original digits as class descriptors, each data value is represented by just two figures: the first is the stem and the second is the leaf, have the advantage of describing individual data values and not just the number in each group
Class interval
Width of each class, the difference between the lower class limit and that of the next highest class
