BUSINESS STATISTICSBQT 173

CHAPTER 1 : DATA & STATISTICS

DATA & STATISTICS

Statistics ???

Meaning :

• Numerical facts

• Field or discipline of study

• Collection of methods for planning experiments, obtaining data and organizing, analyzing, interpreting and drawing the conclusions or making a decision.

1.1 Application in Business

Application in Business

Financial

Economy

Auditing

Production and Operation

Examples present some statistics in business:• Bill Gates is the richest American with a net worth

$43 billion (Forbes, September,30,2002).• A total of 35billion transactions were handled by the

Visa system during 2001 (Forbes, September 16,2002).

• On average, a household carried a credit card balance in $8562 in 2001 (Newsweek, April 1, 2002).

• On average, a wedding in America costs $20,357 (Smart Money, June 2002).

BASIC TERMS IN STATISTICS• Population

- Entire collection of individuals which are characteristic being studied.

• Sample

- Subset of population.

Population

Sample

• Census

- Survey includes every member of population.

• Sample survey

- Collecting information from a portion of population (techniques)

• Element

- Specific subject or object about which information collected.

- Also called as observational units.

• Variable

- Characteristics which make different values.

• Observation

- Value of variable for an element.

• Data Set

- A collection of observation on one or more variables.

Company 2001 Sales (millions of dollars)

Wal-Mart Stores 217,799

IBM 85,866

GENERAL MOTORS 177,260

DELL COMPUTER 31,168

JC PENNEY 32,004

An element or a member An observation or measurement

Variable

Table 1.1 : Charitable Givings of Six Retailers in 2007

QUANTITATIVE AND QUALITATIVE

• Quantitative variable

- A variable that can be measured numerically.

- Data collected on a quantitative variable are called quantitative data.

There are three types of quantitative variables:-

i. Discrete Variable

A variable whose values are countable, can assume only

certain values with no intermediate values.

ii. Continuous Variable

A variable that can assume any numerical value over a

certain interval or intervals.

• Qualitative variable

- A variable that cannot assume a numerical value but can be classified into two or more nonnumeric categories.

- Data collected on such a variable are called qualitative data.

TYPES OF VARIABLESVariable

Quantitative Qualitative

Discrete(e.g, number of

houses, cars accidents

Continuous (e.g., length, age, height,

weight, time)

e.g., gender, marital status

MEASUREMENT SCALES• There are four measurement scales :-

i. Nominal

ii. Ordinal

iii. Interval

iv. Ratio

• Nominal

- only for qualitative classification.

- the weakest data measurement where numbers are used to represent an item / characteristic.

- each data should not be treated as numerical since relative size has no meaning.

- no order or ranking can be imposed on the data.

- e.g : gender – male =1 , female = 2

• Ordinal

- it is possible to rank order all the categories according to some criterion.

- classifies data into categories that can be ranked ( no precise difference )

- example : grades – A,B,C,D and collegiate class – freshman, sophomore, junior, senior.

• Interval

- have the property that the distances between categories are defined by fixed and equal units.

- is ranks of data

- quantity and compare the size of difference between two observations (precise difference do exist)

- example :For age, a change from age 21 to 22 is the same for changes age 31 to 32. Therefore, the interval level of measurement has order and distance.

• Ratio

- The highest level of measurement and allows for all basic arithmetic operations including division and multiplication.

- Has the property that a zero point is naturally defined.

- The mode, mean, median can be used to describe interval and ratio data.

- Poses all the characteristics of interval measurement.

- True zero exist.

- Example : Production of 20 units per hour (ratio level) is twice the production of 10 units per hour.

• Measurement Levels and the Appropriate Averages

ALL DATA

Qualitative data Quantitative data

Nominal

Car makesDays of Week

Gender

Ordinal

TV channelRanks and titleCalendar dates

Interval and Ratio

Sales ($)Accounts Receivable

Market share

Mode Median Mean

1.2 Data

• Data is the collection of the observations or measurements on a variable.

• Data refers to quantitative or qualitative attributes of a variable or set of variables.

- Example :- the whole numbers that represents the scores of students.

• A data with lot of observations usually looks non informative that is we cannot get much information with the raw data.

• Raw data is also called as ungrouped data.

• Data is categorized by two :-

- quantitative data

- qualitative data

• Data should be summarized in more informative way such as graphical, diagrams and charts.

CROSS SECTION VERSUS TIME-SERIES DATA

• Cross Section Data

- Data collected on different elements at the same point in time or for same period of time.

- An example of cross-section data which is giving of six companies for the same period (2007) :-

Company 2007 Charitable Givings (millions of dollars)

Home Depot 42

Macy`s 35.2

Wal-Mart 337.9

Best Buy 31.8

Target 168.9

Lowe`s 27.5

Table 1.2 : Charitable Givings of Six Retailers in 2007

• Time-Series Data

- Data collected on the same element for the same variable at different points in time or for different periods of time.

- Example, a Movieplex with 8 screens would count as 8 toward the total number of screens.

Year Total Indoor Movie Screens

2003 35,361

2004 36,012

2005 37,092

2006 37,776

2007 38,159

2008 38,198

Table 1.3 : Number of Movie Screens

1.3 Data Sources

SOURCES OF DATA

Primary Data-must be collected

(obtained from research)-Methods of collecting primary

data :-i.Personal Interview

ii.Telephone Interviewiii.Questionnaireiv.Observations

Secondary Data

-already collected(published by someone

else)- From books, magazines

STATISTICS

DESCRIPTIVE STATISTICS

DESCRIPTIVE STATISTICS INFERENTIAL

STATISTICS

INFERENTIAL STATISTICS

Using tables, graphs & summarymeasures

Using sample result inmaking decision or predict about a population.

Also called inductive reasoning or inductive statistics.

1.4 Descriptive Statistics

• Consists of methods for organizing, displaying and describing data by using tables, graphs and summary measures.

• In general divided by two categories :-

- Data presentation (display)

- Statistics

1.5 Inferential Statistics

• Consists of methods that use sample results to help make decisions or predictions about a population.

• Area statistics which are deal with decision making procedures.

• Example :-

- In order to find the salary of a college graduate, we may select 2000 recent college graduates, find the starting salaries and make decision based on the information.

1.6 Statistical Analysis using Excel

Example 1.1 :-

Following table shows data for income tax returns for 1995 to 2001 that were filed electronically. Get the sum of income tax for all years and get average of the income tax for those 7 years.

i. Data is key in using Excel.

Figure 1

ii. To get sum of income tax for all years, type =sum(.

iii. Select the range of cells (C4:C10) of numerical data, and close the bracket.

iii. Press enter, the sum should appear.

Figure 2

iii. Press enter, the sum should appear.

iv. To get, the average, the sum should divide by the number of years.

Figure 3

iv. To get, the average, the sum should divide by the number of years.

v. Type AVERAGE(.

vi.Select the range of cells for all years (C4:C10) and close bracket.

vii. Press ENTER. The average of income tax for those years should appear.

Figure 4