Business Statistics : Descriptive Statistics

Ungrouped Data and Grouped Data

Many techniques are presented for reformatting or reducing data so that the data are more manageable and can be used to assist decision makers more effectively.
Two techniques for grouping data are the frequency distribution and the stem-and-leaf plot.
Several graphical tools for summarizing and presenting data, including histogram, frequency polygon, ogive, dot plot, bar chart, pie chart, and Pareto chart for one-variable data and the scatter plot for two-variable numerical data.
Raw data, or data that have not been summarized in any way, are sometimes referred to as ungrouped data.
Data that have been organized into a frequency distribution are called grouped data.
The distinction between ungrouped and grouped data is important because the calculation of statistics differs between the two types of data.

Frequency Distribution

One particularly useful tool for grouping data is the frequency distribution, which is a summary of data presented in the form of class intervals and frequencies.
Frequency distributions are relatively easy to construct.
Although some guidelines and rules of thumb help in their construction, frequency distributions vary in final shape and design, even when the original raw data are identical.
In a sense, frequency distributions are constructed according to individual business researchers’ taste.

When constructing a frequency distribution, the business researcher should first determine the range of the raw data.
The range often is defined as the difference between the largest and smallest numbers.
The second step in constructing a frequency distribution is to determine how many classes it will contain.
After selecting the number of classes, the business researcher must determine the width of the class interval.
An approximation of the class width can be calculated by dividing the range by the number of classes.

Class Midpoint

The midpoint of each class interval is called the class midpoint and is sometimes referred to as the class mark.
It is the value halfway across the class interval and can be calculated as the average of the two class endpoints.
The class midpoint is important, because it becomes the representative value for each class in most group statistics calculations.

Relative Frequency

Relative frequency is the proportion of the total frequency that is in any given class interval in a frequency distribution.
Relative frequency is the individual class frequency divided by the total frequency.
Consideration of the relative frequency is preparatory to the study of probability

Cumulative Frequency

The cumulative frequency is a running total of frequencies through the classes of a frequency distribution.
The cumulative frequency for each class interval is the frequency for that class interval added to the preceding cumulative total.
The concept of cumulative frequency is used in many areas, including sales cumulated over a fiscal year, sports scores during a contest (cumulated points), years of service, points earned in a course, and costs of doing business over a period of time.

Quantitative Data Graphs

One of the most effective mechanisms for presenting data in a form meaningful to decision makers is graphical depiction.
Through graphs and charts, the decision maker can often get an overall picture of the data and reach some useful conclusions merely by studying the chart or graph.
Converting data to graphics can be creative and artful.
Often the most difficult step in this process is to reduce important and sometimes expensive data to a graphic picture that is both clear and concise and yet consistent with the message of the original data.
One of the most important uses of graphical depiction in statistics is to help the researcher determine the shape of a distribution.
Data graphs can generally be classified as quantitative or qualitative.
Quantitative data graphs are plotted along a numerical scale, and qualitative graphs are plotted using nonnumerical categories.

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