Introduction To Statistics

Lecture 01

Dr. MUMTAZ AHMEDMTH 161: Introduction To StatisticsObjectivesStatistics and its importanceBasic Definitions:PopulationsSampleParameterStatisticTwo broad types of statisticsDescriptive StatisticsInferential Statistics2ObjectivesTypes of VariablesQualitative and Quantitative variablesTypes of Qualitative VariablesNominal variablesOrdinal variablesTypes of Quantitative VariablesDiscrete variablesContinuous variablesLevel of measurement of a variableNominal ScaleOrdinal ScaleInterval ScaleRatio Scale3History of StatisticsStatistics is derived from: Latin Word Status means a Political State.

In the past, the statistics was used by rulers and kings. They needed information about lands, agriculture, commerce, population of their states to assess their military potential, their wealth, taxation and other aspects of government.

So theapplicationof statistics was very limited in the past.4What is Statistics?The study of the principles and the methods used in:

CollectingPresentingAnalyzingInterpreting

numericaldata.

5Importance in Daily LifeEvery day we are bombarded with different types of data and claims.

If you cannot distinguish good from faulty reasoning, then you are vulnerable to manipulation and to decisions that are not in your best interest.

Statistics provides tools that you need in order to react intelligently to information you hear or read.

In this sense, statistics is one of the most important things that you can study.

Quote from H.G. Wells (a famous writer) about a century ago: Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.

6Applications of Statistics in Other FieldsStatistics has a number of applications in:

EngineeringEconomicsBusiness and FinanceEnvironmentPhysicsChemistryBiologyAstronomyPsychologyMedical

and so on

7Some Basic Concepts9Before going on, some basic concepts are required:

PopulationSampleParameterStatisticPopulation9A set of all items or individuals of interest.

Examples:All students studying at COMSATSAll the registered voters in PakistanAll parts produced todayTypes Of Population10Finite Population (Countable Population):If it is possible to count all items of population.

Examples:Thenumberof vehicles crossing a bridge every dayThenumberof births per years in a particular hospitalThenumberof words in a bookAll the registered voters in Pakistan (large finite population)

Size of finite Population: Total numberof individuals/units in a finite population (N).Types Of Population11Infinite Population (un-countable population):If it is NOT possible to count all items of a population.

Examples:Thenumberof germs in the body of a patient of malaria is perhaps something which is uncountable Total number of stars in the sky

Sample12A Sample is a subset of the population

Population SampleExamples:1000 voters selected at random for interviewA few parts selected for destructive testingOnly Students of Management Sciences Department

Sample Size : Total numberof individuals/units in sample (n).Note: A good sample is representative of the population. a b c d e f g h i j k l m n o p q r s t u v w x y z

b c g i n o r u y

Parameter and StatisticParameter: A numerical value summarizing all the data of an entire population. e.g. Population Mean, population variance etc.

Statistic : A numerical value summarizing the sample data. e.g. Sample Mean, sample variance etc.

Example:Average income of all faculty members working at COMSATS is a parameter.Average income of faculty members of Management Sciences Department at COMSATS is a statistic.13An Example14A statistics student is interested in finding out something about the average value (in Rupees) of cars owned by the faculty members working at COMSATS.Question: Identify Population, Sample, parameter and statistic.Answer:The population is the collection of all cars owned by faculty members of all departments at COMSATS.A sample can include the cars owned by faculty members of the Management Sciences Department.The parameter is the average value of all cars in the population.The statistic is the average value of the cars in the sample. Parameter and Statistic15Note: Parameters are fixed in value But Statistics vary in value.

Example: If we take a second sample, considering faculty members of English department.Then the average value of these faculty members will be different from the average value of cars obtained for faculty members of Management Sciences Dept.Lesson:Statistic vary from sample to sample.But the average value for all faculty-owned cars, i.e. parameter will not change.Branches of StatisticsStatistics is divided into TWO main branches

Descriptive Statistics

Inferential Statistics16Descriptive StatisticsIt includes tools for collecting, presenting and describing data

Data Collection(e.g. Surveys, Observations or experiments)Data Presentation(e.g. via Graphs and Tables etc.)Data Description(e.g. finding average etc.)17Inferential StatisticsDrawing conclusions and/or making decisions concerning a population based only on sample dataSample statistics Population parameters (known) Inference (unknown, but can be estimated from sample evidence)

18VariableA characteristic that changes or varies over time and/or for different individuals or objects under consideration.

Examples:Hair colorwhite blood cell counttime to failure of a computer component. 19DataAn experimental unit is the individual or object on which a variable is measured.

A measurement results when a variable is actually measured on an experimental unit.

A set of measurements, called data, can be either a sample or a population.20ExamplesExample 1VariableHair colorExperimental unit:PersonTypical MeasurementsBrown, black, blonde, etc.

Example 2Variable Time until a light bulb burns outExperimental unit Light bulbTypical Measurements 1500 hours, 1535.5 hours, etc.21How many variables have you measured?Univariate data:One variable is measured on a single experimental unit (individual or object).

Bivariate data:Two variables are measured on a single experimental unit (individual or object).

Multivariate data:More than two variables are measured on a single experimental unit (individual or object).22Types of VariablesTwo Main types of variables:

Qualitative variables Quantitative variables23Qualitative variablesWhose range consists of qualities or attributes of objects under study.

Examples:Hair color (black, brown, white)Make of car (Suzuki, Honda, etc.)Gender (male, female)Province of birth (Punjab, Sindh, KPK, Balochistan, Gilgit & Baltistan)Grades: (A, B, C, D, F)Level of satisfaction: (Very satisfied, satisfied, somewhat satisfied)Model of transportation: (Car, University Bus, Bike, Cycle etc.)24Quantitative variableswhose range consists of a numerical measurement characteristics of objects under study. Examples:Number of cars owned by faculty of CIITMarks of students of Statistics class in Quiz 1Ages of studentsSalaries of faculty members

25Types of Qualitative variablesThere are TWO main types.

Nominal variable

Ordinal variable26Nominal VariablesA qualitative variable that characterizes (or describes, or names) an element of a population.Examples: Hair color (black, brown, white)Make of car (Suzuki, Honda, etc.)Gender (male, female)Province of birth (Punjab, Sindh, KPK, Balochistan, Gilgit & Baltistan)Note: Order of variables Doesnt matter.27Ordinal VariableOrdinal variableA qualitative variable that incorporates an ordered position, or ranking.

Examples:Grades: (A, B, C, D, F)Level of satisfaction: (Very satisfied, satisfied, somewhat satisfied)28Types of Quantitative variablesThere are TWO types.

Discrete variable

Continuous variable29Discrete VariablesA quantitative variable that can assume a countable number of values. Examples: number of courses for which you are currently registeredTotal number of students in a classNumber of TV sets sold by a company

We cant say there is a half student or half tv set.30Continuous VariableA quantitative variable that can assume an uncountable number of values.

Examples:weight of books and supplies you are carrying as you attend class todayHeight of the studentsAmount of rain fall31Measurement ScalesThe values for variables can themselves be classified by the level of measurement, or measurement scale.

Four Scales of Measurement:Nominal ScaleOrdinal ScaleFor Qualitative DataInterval ScaleRatio ScaleFor Qualitative Data

32Nominal ScaleClassifies data into distinct categories where no ranking is implied. All we can say is that one is different from the other.

Examples:ReligionYour favorite soft drinkYour political party affiliationMode of transportation

Note: Weakest form of measurement. Average is meaning less here. [Question: What is the average RELIGION?]33Ordinal ScaleClassifies values into distinct categories in which ranking is implied.

Examples:Rating a soft drink into: excellent, very good, fair and poor. Students Grades: A, B, C, D, FFaculty Ranks: Professor, Associate Professor, Assistant Professor, Lecturer

Note:It is stronger form of measurement than nominal scaling.It does not account for the amount of the differences between the categories. i.e. ordering implies only which category is greater, better, or more preferrednot by how much.34Interval ScaleA measurement scale possessing a constant interval size (distance) but not a true zero point the complete absence of the characteristic you are measuring.

Example: Temperature measured on either the Celsius or the Fahrenheit scale: Same difference exists between 20o C (68o F) and 30o C (86o F) as between 5o C (41o F) and 15o C (59o F)

Note: You cannot speak about ratios.We cant say that temperature of 300 C is twice as hot as a temperature of 150C.

The arithmetic operation of addition, subtraction, etc. are meaningful.35Ratio ScaleAn interval scale where the sale of measurement has a true zero point as its origin zero point is meaningful.

Examples: height, weight, length, units sold

Note: All scales, whether they measure weight in kilograms or pounds, start at 0. The 0 means something and is not arbitrary.100 lbs. is double 50 lbs. (same for kilograms)$100 is half as much as $200

36ReviewLets review the main concepts:StatisticsDescriptive and InferentialPopulation and sampleVariable typesQualitative and QuantitativeScale of measurementNominalOrdinalIntervalRatio37Next LectureIn next lecture, we will study:Data TypesPrimary DataSecondary DataConcept of SamplingSampling methodsRandom SamplingNon-random SamplingCluster SamplingStratified SamplingSample of Convenience

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