Business Statistics

 Basic Statistical Concepts

❑ The study of statistics can be organized in a variety of ways. 

❑ One of the main ways is to subdivide statistics into two branches: descriptive statistics and inferential statistics. 

❑ To understand the difference between descriptive and inferential statistics, definitions of population and sample are helpful.

❑ Population as a collection of persons, objects, or items of interest. A population is the set of all elements about which we wish to draw conclusions 

❑ A sample is a portion of the whole and, if properly taken, is representative of the whole. A sample is a subset of the elements of a population.

❑ If a business analyst is using data gathered on a group to describe or reach conclusions about that same group, the statistics are called descriptive statistics. Descriptive statistics is the science of describing the important aspects of a set of measurements. 

❑ Another type of statistics is called inferential statistics. Statistical inference is the science of using a sample of measurements to make generalizations about the important aspects of a population of measurements. 

❑ A descriptive measure of the population is called a parameter 

❑ A descriptive measure of a sample is called a statistic.

Data sets , Elements, Variables

The subject of statistics involves the study of how to collect, analyze, and interpret data. Data are facts and figures from which conclusions can be drawn. Such conclusions are important to the decision making of many professions and organizations. For example, 

❑ Economists use conclusions drawn from the latest data on unemployment and inflation to help the government make policy decisions. 

❑ Financial planners use recent trends in stock market prices and economic conditions to make investment decisions. 

❑ Accountants use sample data concerning a company’s actual sales revenues to assess whether the company’s claimed sales revenues are valid. 

❑ Marketing professionals help businesses decide which products to develop and market by using data that reveal consumer preferences. 

❑ Production supervisors use manufacturing data to evaluate, control, and improve product quality. 

❑ Politicians rely on data from public opinion polls to formulate legislation and to devise campaign strategies. 

❑ Physicians and hospitals use data on the effectiveness of drugs and surgical procedures to provide patients with the best possible treatment.

❑ All of them have said that data are facts and figures from which conclusions can be drawn. Together, the data that are collected for a particular study are referred to as a Data set. 

❑ Any data set provides information about some group of individual elements, which may be people, objects, events, or other entities. The information that a data set provides about its elements usually describes one or more characteristics of these elements. 

❑ Any characteristic of an element is called a variable

Cross Sectional and Time Series Data

❑ Some statistical techniques are used to analyze cross-sectional data, while others are used to analyze time series data 

❑ Cross-sectional data are data collected at the same or approximately the same point in time 

❑ For example, suppose that a bank wishes to analyze last month’s cell phone bills for its employees 

❑ Then, because the cell phone costs given by these bills are for different employees in the same month, the cell phone costs are cross-sectional data 

❑ Time series data are data collected over different time periods

Data Source 

Existing Sources :

❑ Sometimes we can use data already gathered by public or private sources. 

❑ The Internet is an obvious place to search for electronic versions of government publications, company reports, and business journals, but there is also a wealth of information available in the reference section of a good library or in county courthouse records.

Experimental and Observational Studies :

❑ There are many instances when the data we need are not readily available from a public or private source. 

❑ The data might not have been collected at all or they may have been collected in a statistically unsound manner. 

❑ In cases like these, we need to collect the data ourselves. 

❑ Suppose we work for a soft drink producer and want to assess consumer reactions to a new bottled water. 

❑ Since the water has not been marketed yet, we may choose to conduct taste tests, focus groups, or some other market research. 

❑ In many marketing, political, and medical situations of these sorts, companies hire outside consultants or statisticians to help them obtain appropriate data. 

❑ Regardless of whether newly minted data are gathered in-house or by paid outsiders, this type of data collection requires much more time, effort, and expense than are needed when data can be found from public or private sources.

Data Measurement

Nominal Level 

❑ The lowest level of data measurement is the nominal level 

❑ Numbers representing nominal level data (the word level often is omitted) can be used only to classify or categorize 

❑ Employee identification numbers are an example of nominal data 

❑ The numbers are used only to differentiate employees and not to make a value statement about them ❑ Some other types of variables that often produce nominal-level data are sex, religion, ethnicity, geographic location, and place of birth. 

❑ Statistical techniques that are appropriate for analyzing nominal data are limited 

❑ However, some of the more widely used statistics, such as the chi-square statistic, can be applied to nominal data, often producing useful information.

 Ordinal Level 

❑ Ordinal-level data measurement is higher than the nominal level 

❑ In addition to the nominal level capabilities, ordinal-level measurement can be used to rank or order objects 

❑ For example, using ordinal data, a supervisor can evaluate three employees by ranking their productivity with the numbers 1 through 3. The supervisor could identify one employee as the most productive, one as the least productive, and one as somewhere between by using ordinal data. 

❑ Because nominal and ordinal data are often derived from imprecise measurements such as demographic questions, the categorization of people or objects, or the ranking of items, nominal and ordinal data are nonmetric data and are sometimes referred to as qualitative data.

Interval Level 

❑ Interval-level data measurement is the next to the highest level of data in which the distances between consecutive numbers have meaning and the data are always numerical 

❑ The distances represented by the differences between consecutive numbers are equal; that is, interval data have equal intervals 

❑ In addition, with interval-level data, the zero point is a matter of convention or convenience and not a natural or fixed zero point 

❑ Zero is just another point on the scale and does not mean the absence of the phenomenon

Ratio Level 

❑ Ratio-level data measurement is the highest level of data measurement 

❑ Ratio data have the same properties as interval data, but ratio data have an absolute zero, and the ratio of two numbers is meaningful 

❑ The notion of absolute zero means that zero is fixed, and the zero value in the data represents the absence of the characteristic being studied 

❑ The value of zero cannot be arbitrarily assigned because it represents a fixed point 

❑ This definition enables the statistician to create ratios with the data 

❑ Because interval- and ratio-level data are usually gathered by precise instruments often used in production and engineering processes, in national standardized testing, or in standardized accounting procedures, they are called metric data and are sometimes referred to as quantitative data.