Presentation on theme: "STATISTIC : INTRODUCTION"— Presentation transcript:
1 STATISTIC : INTRODUCTION Statistic is a discipline of study dealing with(i) collection(ii) analysis(iii) interpretation(iv) presentation of dataTypes of statisticDescriptive statisticUses graphs , charts, tables, calculations of various statistical measuresto summarized and organized information.Examples :list of high and low temperatures for all the states in Malaysiawon/lost percentage for each Malaysian states football teamsthe number of votes a political party receives for each statesfollowing the election week.
2 STATISTIC : INTRODUCTION Inferential StatisticUses a portion of a complete set of population for analysis to reach aconclusion on that particular population. The portion is called a “sample”.Examples:Results of a poll of 600 viewers of NTV7 on how well theylike the shows listed by the TV station.The Survey on drug Abuse by teenagers gives the currentpercentage of young adults using different types of drugs.The percentage are based on National samples.Results on the film “Cicak Man” outstanding sales basedon 200 questionnaires given at several movie outlet to the viewer.
3 STATISTIC : INTRODUCTION Variable, Observation, and Data SetVariableCharacteristics of interest concerning the individual elements of a populationor sample. Often represented by x, y or z.ObservationValue of a variable for one particular element from sample or populationData setContains observations of a variable for the elements of a sample
4 STATISTIC : INTRODUCTION Variable, Observation, and Data Set continue…Example :500 students from a school are polled and each is asked if they approvedor disapproved the University security policies.VariableStudents opinion of the University security policiesObservationThe response “approve” or “do not approved”Data set500 observations
5 STATISTIC : INTRODUCTION Variable, Observation, and Data Set continue…The data set will consist of 500 observations, each one is either 1 or 0.If x is representing the variable then x can be assumes to have 2 values1 or 0.ExerciseFill in the variable, Observation and Data set for the below example situationExample : A survey of 2500 households headed by a single parent is conductedand one characteristic of interest is the yearly household income.VariableObservationData set
6 ExerciseFill in the variable, Observation and Data set for the below example situationExample : A survey of 2500 households headed by a single parent is conductedand one characteristic of interest is the yearly household income.VariableThe yearly household incomeObservationThe amount of household income.Data set2500 observationsIf the variable is represented by y then the values for y would be between thesmallest and the largest yearly household income for the 2500 household.
7 STATISTIC : INTRODUCTION Quantitative Variables : Discrete and ContinuousQuantitativeA quantitative variable is determined when the description of the characteristicof interest results in a numerical way. When measurement is required todescribe characteristic of interest or it is necessary to perform a count todescribe the characteristic.(i) Discrete variableQuantitative variable whose values are countable. Result from counting.See Table 1.0(ii) Continuous variableQuantitative variable that can assume any numerical value over an intervalor several intervals (time). Usually results from making a measurement ofsome type.See Table 1.1
8 STATISTIC : INTRODUCTION Quantitative Variables : Discrete and ContinuousDiscrete VariablesPossible ValuesThe number of defective eggs in a tray of 100 eggs0,1,The numbers of individuals in groups of 30 people with an A blood type0,1,2…30Table 1.0Continuous VariablesPossible ValuesThe length of prison time serve for individuals convicted of first degree murderAll the real numbers between a and b whereby a is the smallest amount of time serve and b is the largest amountThe numbers of death accidents for state of Selangor for the next 6 monthsThe real numbers between a and b whereby a is the smallest amount of accidents and b is the bigest.Table 1.1
9 STATISTIC : INTRODUCTION Quantitative Variables : Discrete and ContinuousExercise : Determine whether the below example are samples Discrete variablesOr Continuous variable.The number of children per household involving 35 low-income households.2. The number of hours spent per week on homework determinedfor 100 student.The level of IQ of a student for a group of student in a class.4. The number of drunk motorist among 100 traffic offenders held at thepolice station.5. The blood pressure readings for 325 hypertensive patients.6. The number of times a machine breakdowns within a year.DiscreteContinuousContinuousDiscreteContinuousContinuous
10 Qualitative Variables STATISTIC : INTRODUCTIONQualitative VariablesA qualitative variable is determined when the description of the characteristic of interest result is a nonnumerical value. Often these nonnumerical values are coded for purposed of computerized statistical analysis. For example Gender might be coded 0 for Female and 1 for Male.See Table 1.2Qualitative VariablesPossible CategoriesMarital StatusSingle, Married, Divorce, SeparatedEmotionsHappy, Sad, Angry, Excited etcPain levelNone, Low, Moderate, SevereGenderMale, FemaleTable 1.2
11 STATISTIC : INTRODUCTION ExerciseWhich of the following are Qualitative data and which are Quantitative data(a) The color of automobiles involved in several severe accidents(b) The length of time required for rats to move through maze(c) The classification of police administrations as city, country, or state(d) The rating given to a pizza in a taste test as poor, good, or excellent(e) The number of times subjects in a sociological research study have been marriedAnswers : a, c, d qualitative: b, e quantitative
12 STATISTIC : INTRODUCTION MeasurementsThere are 4 level of measurements or scale.NominalOrdinalIntervalRatioNominal scale data cannot be arranged in an ordering manner.No arithmetic operations are perform on nominal dataCharacterized by data that consist of names, labels or categoriesSee Table 1.3
13 STATISTIC : INTRODUCTION MeasurementsQualitative VariablesPossible Nominal level data valuesBlood TypesA, B, AB, OState of ResidenceSelangor, Kuala Lumpur, Kelang…ReligionMuslim, Buddha, ChristianTable 1.3OrdinalThe ordinal level is characterized by data that applies categories that can be ranked.Can be arranged in an ordering schemeDifferences between data values either cannot be determined or meaninglessSee Table 1.4
15 STATISTIC : INTRODUCTION MeasurementsIntervalCan be arranged in some order and for which differences in data values are meaningfulResult of counting and measuringArranged in an ordering scheme and differences can be calculated and interpretedRatios are not meaningfulzero measurements does not mean absence of characteristic being measured.
16 Example STATISTIC : INTRODUCTION Measurements Interval: continues… Test scores represent interval data . Limah a student scored 80 on a test and Joyah scored 40 on the same test. Limah scored higher than Joyah did on the test: that is, the test scored can be arranged in order. Limah scored 40 points higher than Joyah did on the test: that is, differences can be calculatedand interpreted. We cannot conclude that Limah knows twice as much as Joyah about the subject matter.A test score 0 does not indicate an absence of knowledge concerning the subject matter.
17 STATISTIC : INTRODUCTION MeasurementsRatioData can be rankedAll arithmetic operation including divisions can be performed (division by0 excluded)Ratio level measurement results from counting or measuringRatio scale data can be arranged in an ordering scheme and differences andratios can be calculated and interpretedA values 0 indicate and absence of characteristic of interest
18 STATISTIC : INTRODUCTION MeasurementsRatio : continues…ExampleThe grams of fat consumed per day for adult in Malaysia is ratio scale data. Johan consumes 50 grams of fat per day and Ahmad consumes 25 grams per day. Johan consumes twice as much fat as Ahmad per day (50/25)=2). For individual who consumes 0 grams of fat on a given day, there is a complete absence of fat consumed on that day. Notice that a ratio is interpretable and an absolute zero exist.
19 STATISTIC : INTRODUCTION ExerciseIndicate the scale of measurement for each of the following variables :Racial originMonthly phone billsBody TemperatureMilitary ranksWeight of studentMovie RatingReligionCalendar numbering of the yearsnominalratiointervalordinalratioordinalnominalinterval
20 STATISTIC : INTRODUCTION Summation NotationLet us explain summation as an example. For instance, supposed the number ofDurian being sold in four days are 300,250,400 and 150. If we let x represent thenumber of Durian sold per day, then the values of the variable for four days arerepresented as follows: x1=300, x2=250, x3=400, x4=150. The sum for the fourdays are then symbolized by x1+x2+x3+x4. The symbol ∑x reads as“the summation of x” is used to represent x1+x2+x3+x4 . The symbol ∑(pronounce as Sigma) stands for “ the sum of”. So the “summation of x” forfour days would be written as ∑x=1100. More example below :∑x = x1+x2+x3+x4+x5 = = 25(∑x)2 = (x1+x2+x3+x4+x5)2 = 252 = 625∑x2 = x12+x22+x32+x42+x52 = = 177∑(x-5) = x1-5+x2-5+x3-5+x4-5+x5-5 = (4-5)+(5-5)+(0-5)+(6-5)+(10-5) = 0