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Statistics – science that deals with the collection, organization or presentation, analysis and interpretation of data.
Origin and Development
 The history of Statistics can be traced back to the Biblical times in Egypt, Babylon and Rome.
 In 3800 BC, the Babylonian government used Statistics to measure the number of men under the king’s rule
and the vast territory that he occupied.
 Modern Statistics is said to have begun with John Graunt (1620 – 1674), an English trademan.
Types Of Statistics
 Descriptive (everyone) – describes the characteristics and properties of a group of persons, place or things.
 Inferential (portion) – test a small portion and use it to generalize for the whole thing.
Data – observation that have been collected.
Population – complete collection of all elements.
Census – collection of data from every member of the population.
Parameter – a numerical measurement describing some characteristic of a population.
(POPULATION -> PARAMETER)
Sample – sub-collection of elements drawn from a population.
Statistic – a numerical measurement describing some characteristic of a sample.
(SAMPLE -> STATISTIC)
Sample data must be collected in an appropriate way, such as through a process of random sampling.
If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of
statistical torturing can salvage them.
Two Categories of Data
1. Quantitative Data (you can perform mathematical operations)
Numbers representing counts or measurements.
Example: weights of supermodels
2. Qualitative Data
Can be separated into different categories that are distinguished by some non-numeric characteristics.
Example: gender (male/female) of professional athletes
Variables – a characteristic or property of a population or sample which makes the members different from each
other.
Example: If a class consists of boys and girls, then gender is a variable in the class.
Classification of Quantitative Variables
1. Discrete Variables
Usually obtained by counting.
Example: number of students in Bio class
2. Continuous Variables
Usually obtained by measurements
Example: weight in kg’s, milk you can get from a cow
Dependent Variables (effect) and Independent Variables (cause)
Example: QUIZ depends on the TIME
Scales of Measurement
1. Nominal Scale – referring to categories
Example: male/female, sections
2. Ordinal Scale – referring to ranking/degree
Example: conduct grade, rank of honor students
3. Interval Scale – data wherein the difference between 2 values is meaningful
Example: numerical grades (exams), years
4. Ratio Scale – zero starting point
Example: weight, height, prices of college textbooks (Php 0.00 represents no cost)
SUMMATION NOTATION (also known as sigma notation)– short way of writing sums.
Examples ...
1.
The summation of x of i from i equals 1 to 3
2.
The summation of y of i from i equals 3 to 6
Properties of Summation
SLOVIN’S FORMULA
To get the sample size,
 ALWAYS ROUND UP
To get the population size,
 ROUND OFF NORMALLY
 If the answer is negative, NOT POSSIBLE
To get the margin of error,
 ROUND OFF NORMALLY
 100 – e = accuracy
Types of Sampling
1. Random Sampling “probability/fair sampling”
 Everyone has an equal chance of being selected.
2. Non-random Sampling “non-probability/bias sampling”
 Not everyone has an equal chance of being selected.
Properties of RANDOM SAMPLING
1. Equiprobability
 Everyone has an equal chance of being selected and included in the sample.
2. Independence
 Chance of one member being chosen does not affect the chance of the others.
2 Kinds of RANDOM SAMPLING
1. Restricted Random Sampling
 Involves certain restrictions intended to improve the validity of the sampling.
 Homogeneity
2. Unrestricted Random Sampling
 Best random sampling design because there were no restrictions imposed.
 Equal chance of being selected.
RANDOM SAMPLING Techniques
1. Lottery or Fishbowl Sampling
 Done by writing the names or numbers of all the members of the population in small rolled pieces of paper
which are later placed in a container.
 The researcher shakes the container thoroughly then draws sample (n) out of population (N) pieces of
paper as desired for a sample.
2. Random Numbers
 Table, calculator, software that generates random numbers.
3. Systematic Sampling
 First, a random starting point is selected then, successive members/elements of the population are drawn.
 Applies to a group of individuals arranged in a waiting line or in a methodical manner.
 If N is known, k value can be calculated as
where N = population size; n = sample size
4. Stratified Sampling
 Members of the population do not belong to the same category, class or group so it is wiser to
employ a stratified technique to give a representative for each group.
Number of students
Simple Stratified
Grade 4
1000
150
5
2500
150
6
1500
150
N = 5000
n = 450
Proportional Stratified
5. Cluster Sampling “area sampling”
 Heterogeneous
NON-RANDOM SAMPLING Techniques
1. Judgment or Purposive Sampling
 Usually based on a certain criteria laid down by the researcher or his adviser.
2. Quota Sampling
 Very similar to stratified random sampling.
 The selection of members of the sample is NOT done randomly.
3. Incidental Sampling
 Applied to samples which are taken because they are the most available.
4. Convenient Sampling
 Convenience it offers to the researcher.
n = 450
Collection of Data
1. Interview Method
 A person-to-person interaction between an interviewer and an interviewee.
 Tape recorded or written
2. Indirect (Questionnaire) Method
 Alternative method
 Written responses are obtained by distributing questionnaires t the respondents.
3. Registration Method
 Enforced by private organizations or government agencies for recording purposes.
4. Observation Method
 Using your senses to observe.
 Scientific method of investigation
5. Experimentation Method
 Objective is to determine the cause and effect of a certain phenomenon.