Lecture Data ans statistics Applications in Business and Economics

Categorical and Quantitative Data
Data can be classified as either categorical or quantitative. Data that can be grouped by
specific categories are referred to as categorical data. Categorical data use either the nominal
or ordinal scale of measurement. Data that use numeric values to indicate how much
or how many are referred to as quantitative data. Quantitative data are obtained using
either the interval or ratio scale of measurement.
A categorical variable is a variable with categorical data, and a quantitative variable
is a variable with quantitative data. The statistical analysis appropriate for a particular variable
depends upon whether the variable is categorical or quantitative. If the variable is
categorical, the statistical analysis is limited. We can summarize categorical data by counting
the number of observations in each category or by computing the proportion of the
observations in each category. However, even when the categorical data are identified by a
numerical code, arithmetic operations such as addition, subtraction, multiplication, and
division do not provide meaningful results. Section 2.1 discusses ways for summarizing
categorical data.
Arithmetic operations provide meaningful results for quantitative variables. For example,
quantitative data may be added and then divided by the number of observations to
compute the average value. This average is usually meaningful and easily interpreted. In
general, more alternatives for statistical analysis are possible when data are quantitative.
Section 2.2 and Chapter 3 provide ways of summarizing quantitative data.
Cross-Sectional and Time Series Data
For purposes of statistical analysis, distinguishing between cross-sectional data and time
series data is important. Cross-sectional data are data collected at the same or approximately
the same point in time. The data in Table 1.1 are cross-sectional because they describe
the five variables for the 25 mutual funds at the same point in time. Time series
data are data collected over several time periods. For example, the time series in
Figure 1.1 shows the U.S. average price per gallon of conventional regular gasoline between
2006 and 2009. Note that higher gasoline prices have tended to occur in the summer
months, with the all-time-high average of $4.05 per gallon occurring in July 2008.
By January 2009, gasoline prices had taken a steep decline to a three-year low of $1.65
per gallon.
Graphs of time series data are frequently found in business and economic publications.
Such graphs help analysts understand what happened in the past, identify any trends over
time, and project future levels for the time series. The graphs of time series data can take
on a variety of forms, as shown in Figure 1.2. With a little study, these graphs are usually
easy to understand and interpret.
For example, Panel (A) in Figure 1.2 is a graph that shows the Dow Jones Industrial
Average Index from 1997 to 2009. In April 1997, the popular stock market index was near
7000. Over the next 10 years the index rose to over 14,000 in July 2007. However, notice
the sharp decline in the time series after the all-time high in 2007. By March 2009, poor
economic conditions had caused the Dow Jones Industrial Average Index to return to the
7000 level of 1997. This was a scary and discouraging period for investors. By June 2009,
the index was showing a recovery by reaching 8700.