# STATISTIC : INTRODUCTION

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STATISTIC : INTRODUCTION
Statistic is a discipline of study dealing with (i) collection (ii) analysis (iii) interpretation (iv) presentation of data Types of statistic Descriptive statistic Uses graphs , charts, tables, calculations of various statistical measures to summarized and organized information. Examples : list of high and low temperatures for all the states in Malaysia won/lost percentage for each Malaysian states football teams the number of votes a political party receives for each states following the election week.

STATISTIC : INTRODUCTION
Inferential Statistic Uses a portion of a complete set of population for analysis to reach a conclusion on that particular population. The portion is called a “sample”. Examples: Results of a poll of 600 viewers of NTV7 on how well they like the shows listed by the TV station. The Survey on drug Abuse by teenagers gives the current percentage of young adults using different types of drugs. The percentage are based on National samples. Results on the film “Cicak Man” outstanding sales based on 200 questionnaires given at several movie outlet to the viewer.

STATISTIC : INTRODUCTION
Variable, Observation, and Data Set Variable Characteristics of interest concerning the individual elements of a population or sample. Often represented by x, y or z. Observation Value of a variable for one particular element from sample or population Data set Contains observations of a variable for the elements of a sample

STATISTIC : INTRODUCTION
Variable, Observation, and Data Set continue… Example : 500 students from a school are polled and each is asked if they approved or disapproved the University security policies. Variable Students opinion of the University security policies Observation The response “approve” or “do not approved” Data set 500 observations

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 values 1 or 0. Exercise Fill in the variable, Observation and Data set for the below example situation Example : A survey of 2500 households headed by a single parent is conducted and one characteristic of interest is the yearly household income. Variable Observation Data set

Exercise Fill in the variable, Observation and Data set for the below example situation Example : A survey of 2500 households headed by a single parent is conducted and one characteristic of interest is the yearly household income. Variable The yearly household income Observation The amount of household income. Data set 2500 observations If the variable is represented by y then the values for y would be between the smallest and the largest yearly household income for the 2500 household.

STATISTIC : INTRODUCTION
Quantitative Variables : Discrete and Continuous Quantitative A quantitative variable is determined when the description of the characteristic of interest results in a numerical way. When measurement is required to describe characteristic of interest or it is necessary to perform a count to describe the characteristic. (i) Discrete variable Quantitative variable whose values are countable. Result from counting. See Table 1.0 (ii) Continuous variable Quantitative variable that can assume any numerical value over an interval or several intervals (time). Usually results from making a measurement of some type. See Table 1.1

STATISTIC : INTRODUCTION
Quantitative Variables : Discrete and Continuous Discrete Variables Possible Values The number of defective eggs in a tray of 100 eggs 0,1, The numbers of individuals in groups of 30 people with an A blood type 0,1,2…30 Table 1.0 Continuous Variables Possible Values The length of prison time serve for individuals convicted of first degree murder All the real numbers between a and b whereby a is the smallest amount of time serve and b is the largest amount The numbers of death accidents for state of Selangor for the next 6 months The real numbers between a and b whereby a is the smallest amount of accidents and b is the bigest. Table 1.1

STATISTIC : INTRODUCTION
Quantitative Variables : Discrete and Continuous Exercise : Determine whether the below example are samples Discrete variables Or Continuous variable. The number of children per household involving 35 low-income households. 2. The number of hours spent per week on homework determined for 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 the police station. 5. The blood pressure readings for 325 hypertensive patients. 6. The number of times a machine breakdowns within a year. Discrete Continuous Continuous Discrete Continuous Continuous

Qualitative Variables
STATISTIC : INTRODUCTION Qualitative Variables A 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 1.2 Qualitative Variables Possible Categories Marital Status Single, Married, Divorce, Separated Emotions Happy, Sad, Angry, Excited etc Pain level None, Low, Moderate, Severe Gender Male, Female Table 1.2

STATISTIC : INTRODUCTION
Exercise Which 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 married Answers : a, c, d qualitative : b, e quantitative

STATISTIC : INTRODUCTION
Measurements There are 4 level of measurements or scale. Nominal Ordinal Interval Ratio Nominal scale data cannot be arranged in an ordering manner. No arithmetic operations are perform on nominal data Characterized by data that consist of names, labels or categories See Table 1.3

STATISTIC : INTRODUCTION
Measurements Qualitative Variables Possible Nominal level data values Blood Types A, B, AB, O State of Residence Selangor, Kuala Lumpur, Kelang… Religion Muslim, Buddha, Christian Table 1.3 Ordinal The ordinal level is characterized by data that applies categories that can be ranked. Can be arranged in an ordering scheme Differences between data values either cannot be determined or meaningless See Table 1.4

STATISTIC : INTRODUCTION
Measurements Qualitative Variables Possible Ordinal level data values Student Performance Poor, Good, Excellent Pain Level None, Low, Moderate, Severe Skills level Beginner, Intermediate, Advanced Table 1.4

STATISTIC : INTRODUCTION
Measurements Interval Can be arranged in some order and for which differences in data values are meaningful Result of counting and measuring Arranged in an ordering scheme and differences can be calculated and interpreted Ratios are not meaningful zero measurements does not mean absence of characteristic being measured.

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 calculated and 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.

STATISTIC : INTRODUCTION
Measurements Ratio Data can be ranked All arithmetic operation including divisions can be performed (division by 0 excluded) Ratio level measurement results from counting or measuring Ratio scale data can be arranged in an ordering scheme and differences and ratios can be calculated and interpreted A values 0 indicate and absence of characteristic of interest

STATISTIC : INTRODUCTION
Measurements Ratio : continues… Example The 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.

STATISTIC : INTRODUCTION
Exercise Indicate the scale of measurement for each of the following variables : Racial origin Monthly phone bills Body Temperature Military ranks Weight of student Movie Rating Religion Calendar numbering of the years nominal ratio interval ordinal ratio ordinal nominal interval

STATISTIC : INTRODUCTION
Summation Notation Let us explain summation as an example. For instance, supposed the number of Durian being sold in four days are 300,250,400 and 150. If we let x represent the number of Durian sold per day, then the values of the variable for four days are represented as follows: x1=300, x2=250, x3=400, x4=150. The sum for the four days 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” for four 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