PROBABILITY and STATISTICS Math-102

Spring semester- 2011

Romasa DawoodRomasa.dawood@gift.edu.pk

P.S. Lecture slides are not substitute for the class lecture or course books.

STATISTICSWhat is Statistics?

Numerical FactsField or

Discipline of study

StatisticsThe consumer price index(CPI) fell by .3% in April (CNBC,

May 16, 2003)From the database of 3458 stock funds, only 172 funds

earned an A rating (Business week, January 27, 2003).At Marriott International, more than 40% of managers

worked their way up through the ranks (Fortune, January 20, 2003)

In Spring Semester, Math-102 class size in GIFT University is ------(GIFT News, march 8,2011).

Numerical facts in preceding statements (.3%, 172, 40%....) are called statistics.

STATISTICSApplication in Business and Economics

Accounting Finance Marketing Production Economics

STATISTICSStatistics is the art and science of collecting,

organizing, analyzing, presenting and interpreting data.

Assignment Q: Keeping in mind the above mentioned definition. Explain to your ‘Nanni Amma’, who faces difficulty in understanding technical terms and lengthy details, how you found out that, the number of female staff in GIFT university, Gujranwala has increased substantially over the past 4 years.

STATISTICSTypes of Statistics

Descriptive StatisticsIt consists of methods of organizing,

summarizing, and presenting data in an informative way.

Inferential StatisticsThe methods used to determine something

about the population on the basis of a sample.

STATISTICSCONCEPTS

DataData are those facts or figures that we collect, analyze and summarize for

presentation and interpretation.

Elements/memberElements are the entities on which data is collected.

VariableVariable is a characteristic of interest for the elements.

ObservationThe set of measurements obtained for a particular element is called an

observation.

PopulationThe set of all units of interest (finite or infinite). E.g. all students at GIFT

University, Gujranwala.

SampleA subset of the population actually observed. E.g. students in MATH- 102

class.

Types of DataData: A Set of measurementsQualitative DataQuantitative Data

ContinuousDiscreet

Based on the time they are collected, data can be classified as either cross-section, time series or panel data

Cross-section DataTime series DataPanel Data

Types of DataData: A Set of measurementsQualitative DataQualitative Data includes labels or names used to identify an

attribute of each element. E.g. Gender, Hair Color, Attitude towards war or capital punishment.

Quantitative DataQuantitative Data requires numeric values that indicate how

much or how many. A variable that can be measured numerically is called quantitative variable. Discrete, e.g. number of children, number of cars owned

by a familyContinuous. e.g. distance, temperature, time( between 30

and 40 mins), length, height

Types of DataData: A Set of measurementsCross-Sectional DataA cross-sectional data set consists of a sample of

individuals, households, firms, cities, states, countries, or a variety of other units, taken at a given point in time. E.g. the information on incomes of 100 families for 2005 is an example of cross-section data.

Time-series DataA time series data set consists of observations on a variable

or several variables over time. E.g. stock prices, money supply, consumer price index, gross domestic product, annual homicide rates, and cell phones sales figures.

Panel DataA panel data (or longitudinal data) set consists of a time

series for each cross-sectional member in the data set.

Cross section Data

Time Series Data

Panel Data

Levels of MeasurementData: A Set of measurementsThere’re four types of levels of measurement

1. Nominal level data2. Ordinal Level data3. Interval Level data4. Ratio level data

Levels of Measurement

Data: A Set of measurementsQualitative Data

Nominal, e.g. Binary (head, Tail), (Male, Female), hair color: black, golden, brown.

Ordinal, e.g. attitude to war or capital punishment: Strongly agree, Agree, Neutral, disagree, strongly disagree.

A qualitative variable is a variable with qualitative data.

Example on the Levels of MeasurementPizza Hut, Gujranwala asks their customers to rate the quality

of services.

How would you rate the quality of our services?Poor….Fair….Average……Good ….Excellent

orPizza Hut, Gujranwala asks respondents to rate the quality of

the service on a five-point scale (1-5) as:1 for poor2 for fair3 for average4 for good5 for excellent

We can reverse the coding method 1 for excellent and 5 for poor.

Levels of MeasurementData: A Set of measurementsQuantitative Data

Interval, e.g. Fahrenheit temperatureRatio (real zero), e.g. distance, number of

children

A quantitative variable is a variable with quantitative data.

Interval level DataQuantitative Data

Interval, e.g. Fahrenheit temperature

The third level of Data is interval data. One can say the temperature scales. E.g. 25 0C is warmer than 200C by exactly 50C. Also we can say that 250C is cooler than 300C by 50C.

But we cannot say that 300C is twice as warm as 150C because temperature measured in Celsius does not have an absolute zero point. That is the zero point is arbitrarily chosen and 00C shows some level of temperature. If we consider Fahrenheit in which 32 F corresponds to 00C and 68 F corresponds to 20 C and 500C corresponds 10 F then we cannot say that 200c is twice as warm as 100C

Interval level DataInterval Data provide not only greater than or

less than information, but also details on how much greater than or less than.

Interval data have no absolute zero point. So that we cannot use comparisons such as ‘twice as many’ or ‘half as much’ with interval data.

Ratio level DataHow many e-mail messages did you send

yesterday?How old are you?

The answer for both questions provides details about how much greater or less. They have an absolute zero point: 0 message means no message.

Sources of DataExisting Sources

Internal sources; such as companies own personnel files accounting records.

External sources; Organizations that specializes in collecting and maintaining data make available substantial amounts of business and economic data. E.g. Dow jones & company, Dun and Bradstreet, Bloomberg provide extensive business database to clients.

InternetGovernment Agencies

Statistical StudiesAt times data needed for a particular study is not available

through existing sources. Then usually statistical studies are conducted. They’re either experimental or observational.

Experimental studyHow a new drug affects blood pressure?

Observational/Non experimental studyStudies of smokers and non smokers are

observational studies as researchers do not attempt to control or determine who will smoke and who will not smoke.

Example 1

1. How many elements this data set contains?2. Which of the variable are quantitative and which are

qualitative?3. What is the average CD capacity for the sample?4. What percentage of the minisystem provides an FM

tuning rating of very good or excellent?5. What percentage of the minisystem includes two tape

decks?

Example 2State whether each of the following variable is

qualitative or quantitative and indicate its measurement scale.1. Age2. Gender3. Class Rank4. Make of Automobile5. Number of people favoring the death penalty6. Annual Sales7. Soft drink size ( small, medium, large)8. Employee Classification ( GS1 through GS18)9. Earning per share10. Method of payment( Cash, Check, Credit Card)

Example 3.What is your monthly pocket money?

0---10001500-25003000-45005000 & above

Example 3Regarding the monthly pocket moneyYou may think of an absolute zero point for

pocket money as no pocket money at allYou may think of comparisons, 1500 Rs is

twice as much as 3000 Rs.That leads you to deciding that pocket

monies are ratio data. But it is not Ratio Data

Example 3Reason

Respondents are asked to place themselves into one of the four categories of pocket money, so we can code these categories from 1 to 4 with 1 for the lowest and 4 for the highest amount.

If you are in the second category and Ayesha in the first we know that your income is higher than Ayesha, but we don’t know exactly how much higher, we cannot say as much as twice, therefore, in this case, we are collecting ‘Ordinal Data’.

ReferencesLind, A. Douglas, William G. Marchal and

Samuel A. Wathen, Basic Statistics for Business & Economics, 13th Edition, McGraw Hill/Irwin Publishing.

Mann, Prem S., Introductory Statistics, Sixth Edition 2005, John Wiley & Sons, Inc., Noida.

Anderson, Sweeney, Williams “Statistics for Business and Economics” 9th edition 2005 Thomson South-Western