Lecture Data ans statistics Applications in Business and Economics

Data Acquisition Errors
Managers should always be aware of the possibility of data errors in statistical studies. Using
erroneous data can be worse than not using any data at all. An error in data acquisition occurs
whenever the data value obtained is not equal to the true or actual value that would be obtained
with a correct procedure. Such errors can occur in a number of ways. For example, an
interviewer might make a recording error, such as a transposition in writing the age of a
24-year-old person as 42, or the person answering an interview question might misinterpret
the question and provide an incorrect response.
Experienced data analysts take great care in collecting and recording data to ensure that
errors are not made. Special procedures can be used to check for internal consistency of the
data. For instance, such procedures would indicate that the analyst should review the accuracy
of data for a respondent shown to be 22 years of age but reporting 20 years of work
experience. Data analysts also review data with unusually large and small values, called
outliers, which are candidates for possible data errors. In Chapter 3 we present some of the
methods statisticians use to identify outliers.
Errors often occur during data acquisition. Blindly using any data that happen to be
available or using data that were acquired with little care can result in misleading information
and bad decisions. Thus, taking steps to acquire accurate data can help ensure reliable
and valuable decision-making information.
1.4 Descriptive Statistics
Most of the statistical information in newspapers, magazines, company reports, and other
publications consists of data that are summarized and presented in a form that is easy for
the reader to understand. Such summaries of data, which may be tabular, graphical, or
numerical, are referred to as descriptive statistics.
Refer again to the data set in Table 1.1 showing data on 25 mutual funds. Methods of
descriptive statistics can be used to provide summaries of the information in this data set.
For example, a tabular summary of the data for the categorical variable Fund Type is
shown in Table 1.4. A graphical summary of the same data, called a bar chart, is shown
in Figure 1.5. These types of tabular and graphical summaries generally make the data easier
to interpret. Referring to Table 1.4 and Figure 1.5, we can see easily that the majority
of the mutual funds are of the Domestic Equity type. On a percentage basis, 64% are of
the Domestic Equity type, 16% are of the International Equity type, and 20% are of the
Fixed Income type.
A graphical summary of the data for the quantitative variable Net Asset Value, called
a histogram, is provided in Figure 1.6. The histogram makes it easy to see that the net asset
values range from $0 to $75, with the highest concentration between $15 and $30. Only
one of the net asset values is greater than $60.
In addition to tabular and graphical displays, numerical descriptive statistics are used
to summarize data. The most common numerical descriptive statistic is the average, or
mean. Using the data on 5-Year Average Return for the mutual funds in Table 1.1, we can
compute the average by adding the returns for all 25 mutual funds and dividing the sum
by 25. Doing so provides a 5-year average return of 16.50%. This average demonstrates a
measure of the central tendency, or central location, of the data for that variable.
There is a great deal of interest in effective methods for developing and presenting descriptive
statistics. Chapters 2 and 3 devote attention to the tabular, graphical, and numerical
methods of descriptive statistics.