Chap 2-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Theme 2 Describing Data: Graphical Statistics for Business and Economics 6 th Edition

Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 2-2 Theme Goals After completing this theme, you should be able to: Identify types of data and levels of measurement Create and interpret graphs to describe categorical variables: frequency distribution, bar chart, pie chart, Pareto diagram Create a line chart to describe time-series data Create and interpret graphs to describe numerical variables: frequency distribution, histogram, ogive, stem-and-leaf display Construct and interpret graphs to describe relationships between variables: Scatter plot, cross table Describe appropriate and inappropriate ways to display data graphically

Variables & Types of Data In order to gain information about seemingly haphazard events, statisticians study random variables. A variable is a characteristic or attribute that can assume different values. Height, weight, temperature, etc are examples of variables. Variables can be classified as categorical (qualitative) or numerical (quantitative)

Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 2-4 Types of Data Data CategoricalNumerical DiscreteContinuous Examples: Marital Status Are you registered to vote? Eye Color (Defined categories or groups) Examples: Number of Children Defects per hour (Counted items) Examples: Weight Voltage (Measured characteristics)

Categorical variables Qualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. For example, if subjects are classified according to gender (male or female), then the variable "gender" is categorical. Other examples of qualitative variables are religious preferences, marital status and geographic locations

Numerical variables Quantitative variables are numerical in nature and can be ordered or ranked. For example, variable "age" is numerical, and people can be ranked according to the value of their ages – the number of years lived. Numerical variables can be further classified into two groups, discrete or continuous

Discrete or continuous Discrete variables can be assigned values such as 0, 1, 2, 3, and are said to be countable. Examples of discrete variables are the number of children in a family, the number of students in a classroom. Discrete variables assume values that can be counted

Continuous variables Continuous variables can assume all values between any two specific values. They are obtained by measuring. Temperature, for example, is a continuous variable, since the variable can assume it values between any two given temperatures. Continuous variables can assume all values between any two specific values

Data The measurements or observations (values) for a variable are called data, and a collection of data values forms data set. Each value in the data set is called a data value or a datum

Measurement scales In addition to being classified as qualitative or quantitative, variables can also be classified by how they are categorized, counted, and measured. This type of classification uses measurement scales, and four common types of scales are used: nominal, ordinal, interval, and ratio

Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 2-11 Measurement Levels Interval Data Ordinal Data Nominal Data Quantitative Data Qualitative Data Categories (no ordering or direction) Ordered Categories (rankings, order, or scaling) Differences between measurements but no true zero Ratio Data Differences between measurements, true zero exists

The nominal level of measurement classifies data into mutually exclusive, exhaustive categories in which no order or ranking can be imposed on the data

Nominal A sample of college instructors classified according to subject taught (English, history, psychology, or mathematics) is an example of nominal-level measurement. Survey subjects classified as male or female is another example of nominal- level measurement

Ordinal The ordinal level of measurement classifies data into categories that can be ranked; however, precise differences between the ranks do not exist

Ordinal Examples of ordinal-measured data are letter grades (А, В, C, D, E, F), rating scales and rankings

Interval The interval level of measurement ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero

Interval Temperature is an example of interval measurement, since there is a meaningful difference of one degree between each unit, such as 36 degrees and 37 degrees. One property is lacking in the interval scale: There is no true zero

Ratio The ratio level of measurement possesses all characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist between different units of measure

Ratio For example, if one person can lift 200 pounds and another can lift 100 pounds, then the ratio between them is 2 to 1. Put another way, the first person can lift twice as much as the second person

Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 2-20 Graphical Presentation of Data Data in raw form are usually not easy to use for decision making Some type of organization is needed Table Graph The type of graph to use depends on the variable being summarized

Organizing data When conducting a statistical study, the researcher must gather data for the particular variables under study. For example, if a researcher wishes to study the number of people who buy chocolate in a specific geographic area, he or she would have to gather the data from various department stores, shops, kiosks

Organizing data In order to describe the situation, draw conclusions about people buying chocolate, the researcher must organize the data in some meaningful way. The most convenient method, organizing data is to construct a frequency distribution

Graphs After organizing the data, the researcher must present it so that it can be understood by those who will benefit from reading the study. The most useful method of presenting the data is by constructing statistical charts, tables and graphs. There are many different types of charts & graphs, and each one has a specific purpose

Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 2-24 Graphical Presentation of Data Techniques reviewed in this chapter: Categorical Variables Numerical Variables Frequency distribution Bar chart Pie chart Pareto diagram Line chart Frequency distribution Histogram and ogive Stem-and-leaf display Scatter plot (continued)

Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 2-25 Tables and Graphs for Categorical Variables Categorical Data Graphing Data Pie Chart Pareto Diagram Bar Chart Frequency Distribution Table Tabulating Data

Graphs The purpose of this lecture is to explain how to organize data by constructing frequency distributions and how to present the data by constructing charts and graphs. The charts & graphs illustrated in this presentation include histograms, frequency distribution polygons, ogives, bar and pie graphs

Grouping data Grouping of data is partition of population into classes. Grouping is classified as typological, structural and analytical

Typological Grouping Typological grouping is partition of heterogeneous population into some classes (homogeneous classes) by socio-economic types. For example, below is the grouping of enterprises by pattern of ownership (table 1). The population of enterprises is heterogeneous. When we part the population, we form homogeneous classes

Pattern of ownership The number of enterprises count - thousandspercent State ownership 135,02,82,8 Municipal ownership 257,65,4 Private ownership 3975,583,383,3 Joint ownership 206,44,4 Public ownership 197,44,1 Total 4771, Source:: Россия в цифрах. 2009: Краткий статистический сборник. - Москва, 2009, с Table 1

Structural Grouping Structural grouping is partition of homogeneous population into some classes, which characterize its structure. Table 2 shows the distribution of population of the Russian Federation by per capita average money income as an example of structural grouping

31 Source:: Total population in 2008, mid-year estimation millionspercent 141,95100,0 of which with average per capita monthly money income, RUR: less than 2000,0 2,131,51,5 2000,1-4000,0 11,788,38,3 4000,1-6000,0 17,0312,012,0 6000,1-8000,0 17,1812,112,1 8000, ,0 15,4710,910, , ,0 28,5320, , ,0 28,3920,0 over 25000,0 21,4315,1 Table 2

Structural Grouping For constructing another structural grouping, we can use the data from table 1. We will part only homogeneous population such as the class of private ownership enterprises. Consider the example of structural grouping of private enterprises by number of personnel in table 3.

33 Source:: Imputations from the Table 1 Number of personnel Number of enterprises count - thousands percent up to ,634, ,422, ,518,218, ,713,613,6 more than ,2453,211,411,4 Total 3975,5100,0 Table 3

Structural Grouping This grouping shows the distribution of enterprises inside the homogeneous population (by pattern of ownership) and characterizes the position of each class. It means the enterprises which have the number of personnel of up to 50 people take 34.1% or maximum weight

Analytical Grouping Analytical grouping is grouping which discovers the regularities between the examined processes and their attributes. Using the data of banks' activity, we can construct the analytical grouping (table 4)

36 Source:: Conditional data The size of net income The number of banks, units Net income per one bank Assets holding per one bank ,00601, ,88551, ,93589, ,24608,76 Total20 25,27588,55 Table 4

Basis of grouping The important moment is the allocation of the basis of the grouping, which there should be a resulting or dependent parameter. In this case, resulting parameter can be an assets holding. The second important moment is definition of influencing parameters, in our opinion, influence on the resulting parameter. Influencing parameter as located in the left column of the table. It is the basis of grouping

38 Table 5 Seniority, years Wage, RUR less than and more30 800

Duration of contractual relations of a department store with suppliers, years Number of suppliers The share of high-quality production,% countpercent before – – more than Total , :10:4039

To be continued