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