2. Introduction to Statistics
Statistics is a branch of Applied Mathematics
specializing in procedures for collecting,
organizing, presenting, analyzing, and
interpreting data from observations.
3. Introduction to Statistics
Statistics involves much more than simply drawing
graphs and computing averages.
In education, it is frequently used to describe test results.
In science, the data resulting from experiments must be collected and analyzed.
Manufacturers can provide better products at reasonable costs through the use of
statistical quality control techniques.
In government, many kinds of statistical data are collected all the time.
A knowledge of statistics can help you become more critical in your analysis of
information; hence, you will not be misled by manufactured polls, graphs, and
averages.
4. A statistical question is one that can be
answered by collecting data that vary.
Example of Statistical Questions:
1. How many hours do college students spend
time in studying? (Summarizing question)
2. Do college students spend more time in social
media than studying? (Comparing question)
3. Do students who spend more time in studying
do better in exam? (Relationship question)
Example of Non-Statistical
Questions:
1. How old are you?
2. What is your favorite
subject?
3. How many siblings
does Elise have?
5. Descriptive – gathering,
classification and
presentation of data and
the collection of
summarizing values to
describe group
characteristics of data.
Inferential – methods
dealing with making
inference, estimates or
prediction about a large set
of data
6. DESCRIPTIVE
STATISTICS
Commonly Used Summarizing Values
Percentage
Measures of Central Tendency and Location
Measures of Variability
Skewness and Kurtosis
INFERENTIAL
STATISTICS
Examples
Class average of examination
Range of students’ scores
Average salary
Commonly Used statistical tools or techniques
Estimation of Parameters
Testing of Hypothesis
(z-test, t-test, ANOVA, Chi-squares, regression,
Time series analysis)
Examples
Significant Relationship between job satisfaction
and performance of CCDC employees
The use of module is significantly effective than the
traditional method of teaching
7. There are two types of data: numerical(quantitative) and
categorical(qualitative).
1. NUMERICAL/QUANTITATIVE DATA – numerical
values
2. QUALITATIVE/CATEGORICAL DATA – categorical
responses such as colors, information, or questions
that are answerable by YES or NO, labels, gender,
attitude, etc.
8. Variable – numerical characteristics or attributes associated
with the population that can assume different values.
1. Discrete – finite number of values; values are obtained
by counting
2. Continuous – infinite number of values between two
specific numbers; values are obtained by measuring
QUANTITATIVE
Discrete Continuous
9. Examples
1. Number of students in the Criminology Department
2. The result of rolling a die
3. The distance from Tiong San to SM
4. The heights of CCDC varsity players
QUANTITATIVE
Discrete Continuous
10. 2. QUALITATIVE/CATEGORICAL DATA take nonnumerical values, such as colors,
information or questions that are answerable by YES or NO, labels, etc.
(example: large, medium, and small)
1. Since our country is infected with Corona Virus, do you follow the health
protocols given by the Department of Health?
2. Matcha is my favorite milktea flavor.
3. Blue signifies calmness, tranquility, relaxation and peace.
11. classifies and
categorizes data
rank or order to
show relationship
value of zero or
starts at an absolute
zero point
variables are
measured based on
a set of intervals on
a certain scale
Levels of Measurement
Nominal Ordinal Ratio Interval
Type of blood
Gender
Religion
President(Officers)
Eldest(Family order)
Mass, Length, Time
Angle, Energy, Rating
Electrical Charge
Test Results
Pressure
Temperature
(Freezing Point,
Boiling Point)
Examples
12. COLLECTION OF DATA
Statistical Instruments
Observation- it focuses in determining the changes in the attitude,
characteristics and behavior of people or other subjects. This
technique includes watching and recording actions and behaviors.
The person who gathers the data is called an investigator while the
person being observed is called the subject.
Interviews- oral or verbal communication where the interviewer asks
questions in any mode (face to face, telephone, or virtual) to an
interviewee.
13. Questionnaire- gathered through a set of question that is mailed or handed to
respondents who are expected to read and understand them.
Survey –if you have big number of samples, it is the most practical way to use.
in a national level, surveys are usually covered by the government and other
forms of surveying organization such as Philippine Statistics Authority (PSA).
Experiment Method – this method is used when the objective is to determine
the cause and effect relationship of a certain phenomenon under controlled
condition.
COLLECTION OF DATA
Statistical Instruments
14. A population includes all of the
elements from a set of data: objects,
events, organizations, countries,
species, organisms, etc.
A sample is a subset taken from a
population, either by random
sampling or by non-random
sampling.
COLLECTION OF DATA
Sampling Techniques
15. A POPULATION includes all of the elements from a set of data:
objects, events, organizations, countries, species, organisms, etc.
A SAMPLE is a subset taken from a population, either by random
sampling or by non-random sampling.
COLLECTION OF DATA
Sampling Techniques
16. SAMPLING TECHNIQUES
A. Random Sampling
➢selection of n elements derived from the N population, which is the
subject of an investigation or experiment, where each point of the
sample has an equal chance of being selected using the
appropriate sampling technique
Types of Random Sampling Techniques
1. Lottery sampling - each member of the population has an equal
chance of being selected.
17. SAMPLING TECHNIQUES
A. Random Sampling
2. Systematic sampling –members of the population are listed and samples
are selected at intervals called sample intervals. In this technique, every nth
item in the list will be selected from a randomly selected starting point.
Example
if we want to draw a 200 sample from a population of 6,000, we can select
every 3rd person in the list. In practice, the numbers between 1 and 30 will be
chosen randomly to act as the starting point.
18. SAMPLING TECHNIQUES
A. Random Sampling
3. Stratified random sampling – members of the population are grouped on
the basis of their homogeneity. This technique is used when there are number
of distinct subgroups in the population within which full representation is
required. The sample is constructed by classifying the population into
subpopulations or strata on the basis of certain characteristics of the
population, such as age, gender or socio-economic status. The selection of
elements is then done separately from within each stratum, usually by random
or systematic sampling methods.
19. SAMPLING TECHNIQUES
A. Random Sampling
3. Stratified random sampling
Example: Using stratified random sampling,
select a sample of 400 students from the
population which are grouped according to
the cities they come from. The table shows
the number of students per city.
Solution: To determine the number of students to be taken as sample
from each city, we divide the number of students per city by total
population (N= 28,000) multiply the result by the total sample size
(n= 400).
20. Example: Using stratified random sampling,
select a sample of 400 students from the
population which are grouped according to
the cities they come from. The table shows
the number of students per city.
Solution: To determine the number of students to be taken as sample
from each city, we divide the number of students per city by total
population (N= 28,000) multiply the result by the total sample size
(n= 400).
SAMPLING TECHNIQUES
A. Random Sampling
3. Stratified random sampling
21. SAMPLING TECHNIQUES
A. Random Sampling
4. Cluster sampling – applied on a geographical basis. Generally, first sampling
is performed at higher levels before going down to lower levels. For example,
samples are taken randomly from the provinces first, followed by cities,
municipalities or barangays, and then from households.
5. Multi-stage sampling uses a combination of different sampling techniques.
For example, when selecting respondents for a national election survey, we can
use the lottery method first for regions and cities. We can then use stratified
sampling to determine the number of respondents from selected areas and
clusters.
