Instructional material in Statistics and Probability

1. PREPARED BY:
LEVIGILDA B. CARBOS
SHS-TII
CASTILLEJOS NATIONAL HIGH
SCHOOL

2. LESSON - OBJECTIVES:
The learners are expected to understand how to:
Define what is statistics
Understand statistics key concepts
Determine the essential processes involve in doing statistics
Identify data and to classify them
Use appropriate scales of data measurement

3. WHAT IS STATISTICS?
Statistics – is the science that deals
with the collection, organization
and presentation, analysis and
interpretation of all kinds of data
pertinent to the study being
considered.

4. 2TYPES OF STATISTICS
DECRIPTIVE STATISTICS – is a group of
statistical measurements that aims to
provide the basic characteristics of a data
through tables and graphs and other
descriptive measures such as measures of
central tendency, measures of position,
and measures of variation.
DECRIPTIVE STATISTICS – is a group of
statistical measurements that aims to
provide the basic characteristics of a data
through tables and graphs and other
descriptive measures such as measures of
central tendency, measures of position,
and measures of variation.

5. 2TYPES OF STATISTICS
INFERENTIAL STATISTICS – aims to infer
or to make interpretations by making a
concluding statement about the population
based on the result derived from a data set.
Measures commonly used in inferential
statistics include: Analysis ofVariance
(ANOVA), t-test, chi-square test,
correlation and regression analysis. .

6. 1. Collection of Data
– refers to the gathering of related
information such as:
(a) what is useful and needed;
(b) where to get information and
(c) how to get information

7. 2. Organization and Presentation of Data –
refers to the systematic way of organizing data. It
involves the following:
(a) Collecting;
(b) Classifying and arraying, and
(c) Presenting data gathered in preparation to its
analysis.

8. 3. Analysis of Data – refers to extracting relevant
information the systematic way of organizing data. It
involves the following:
(a) Comparison and contrast;
(b) Description, and
(c) Statistical measurements to come up with
numerical values and qualitative summary as a
resulting conclusion.

9. 4. Interpretation of Data – refers to the drawing
of logical statements from the analyzed
information. In involves the following:
(a) Generalizing;
(b) Forecasting, and
(c) Recommending solutions and interventions
about the study.

10. 2 MAJORTERMS USED IN STATISTICS
DATA – is a body of information or observations being
considered by the researcher.When data is processed,
information, which is the basis for decision making is
produced.
VARIABLE – is used to define certain observable values or
characteristics. It is called variable since the characteristics
vary from one another.The values of the variable are the
possible observable values or characteristics of the variable.
These values are the data to be processed.

11. DIFFERENT WAYS OF CLASSIFYING DATA
ACCORDINGTO NATURE
 QUANTITATIVE or NUMERICAL DATA are those obtained
from variables which are in the form of numbers e.g. age,
height, amount.
QUALITATIVE or CATEGORICAL DATA are those obtained
from variables which are in the form of categories,
characteristics, names or labels, e.g. gender, socio-economic
status, civil status.

12. DIFFERENT WAYS OF CLASSIFYING DATA
ACCORDINGTO SOURCE
 PRIMARY DATA are first-hand information, e.g. data
gathered from a survey, where the person who
collected the data is the one using it.
SECONDARY DATA are second-hand information
e.g. information from newspapers or journals,
economic indicators.The data being used are
collected by another person or organization.

13. DIFFERENT WAYS OF CLASSIFYING DATA
ACCORDINGTO ARRANGEMENT
 UNGROUPED DATA are data without specific
order or arrangement.They are referred to as raw
data.
GROUPED DATA are data arranged or tabulated
and presented in an organized manner.

14. QUANTITATIVE DATA CLASSIFIED
ACCORDINGTO MEASUREMENT
DISCRETE DATA are those obtained from counting
process where data are whole numbers, e.g.
household size, number of cans of sardines
produced.
CONTINUOUS DATA are those obtained through
the measuring process where the data are values
that may be decimals or fractions, e.g. inflation rate,
weight in kilograms.

15. FOUR SCALES OF DATA MEASUREMENT
(ALSO REFERREDTO AS LEVELS OF DATA)
1. NOMINAL SCALE is the lowest level of data
measurement where the values for the variables
are used for identification purposes only and it
does not signify any quantitative value.To record
nominal data, numbers are arbitrarily assigned to
each category.

16. FOUR SCALES OF DATA MEASUREMENT
(ALSO REFERREDTO AS LEVELS OF DATA)
1. NOMINAL SCALE
Examples: marital status in a survey questionnaire
may include the following values: single,
married/living with partner, widowed, separated.
To encode the responses, values may be assigned
as follows: 1 for single, 2 for married, 3 for
widowed and 4 for separated.

17. FOUR SCALES OF DATA MEASUREMENT
(ALSO REFERREDTO AS LEVELS OF DATA)
2. ORDINAL SCALE has all the properties of the nominal
scale, but the numbers obtained also gives the order of the
values. It is used only in variables tha involves ranking
process.
For Example:
If the variable is positions in the company, the possible
responses may be managerial, supervisory and rank and
file. Managerial position may be assigned a value of 1,
supervisory 2, and rank and file 3.

18. FOUR SCALES OF DATA MEASUREMENT
(ALSO REFERREDTO AS LEVELS OF DATA)
3. INTERVAL SCALE has all the properties of the
ordinal scale.The intervals between values in a set of
interval data are consistent and meaningful, but it
does not involve a true zero point. Furthermore, since
they ar real numbers, all calculations can be
performed.
For Example:
IQ scores of students in a grade 11 class.

19. FOUR SCALES OF DATA MEASUREMENT
(ALSO REFERREDTO AS LEVELS OF DATA)
4. RATIO SCALE has all the properties of the
interval scale.In this level there is a true zero point
(an absolute value of zero) and multiplication and
division of measurements can be performed.
For Example:
Height and weight.

20. FOUR SCALES OF DATA MEASUREMENT
(ALSO REFERREDTO AS LEVELS OF DATA)
Note:
Interval and Ratio scales are the
highest level of data measurement
because all calculations involving the
data sets are valid.

21. SUMMARY OFVARIOUS DATA
CLASSIFICATIONS AND RELATIONSHIPS

22. EXERCISES:
CLASSIFY EACH ITEM ACCDG.TO NATURE
_______ 1. CONTROL NUMBER
_______ 2. MARITAL STATUS
_______ 3. NUMBER OF CHILDREN
_______4. EDUCATIONAL ATTAINMENT
_______ 5. OCCUPATION
_______ 6. AVERAGE GROSS MONTHLY INCOME
_______ 7.YEARS OF SERVICE INTHE COMPANY
_______8. NUMBER OF HOURS SPENT DAILY CHATTING ONLINE
_______9. NUMBER OF GLASSES OF WATERTAKEN DAILY
_______10. EXTENT BY WHICH STUDY HABITS AFFECTS THE PERFORMANCE OF A STUDENT.

23. COMPLETETHETABLE BY CLASSIFYINGTHE DATA ACCDG.
TO NATURE. IF DATA IS QUANTITATIVE, CLASSIFY FURTHER
ACCDG.TO MEASUREMENT.
A VARIABLES ACCORDINGTO NATURE
ACCORDINGTO
MEASUREMENT
1 ID NUMBER OF STUDENTS
2 NO. OF PAGES IN A BOOK
3 DATE OF BIRTH
4 MODEL OF CELLPHONE USED
5 NUMBER OFTEXT MESSAGES SENT DAILY
6 DAILY ALLOWANCE
7 COMPUTER RENTAL FEE
8 KILOWATT HOURS USED PER MONTH
9 NO. OF STUDENTS PER CLASS
10 MONTHLY EXPENSES FOR INTERNET USED
E
E
E
E
E
E
E
E

24. EXERCISES:
CLASSIFY EACH ITEM ACCDG.TOTHE FOUR SCALES OF DATA MEASUREMENT.
(ALSO REFERREDTO AS LEVELS OF SCALE).
_______ 1. MONTHLY SALES IN A SCHOOL CANTEEN.
_______ 2. ZIP CODE
_______ 3. SCORES IN A MATHEMATICS QUIZ
_______4. SOCIO-ECONOMIC STATUS (A,B,C,D,E)
_______ 5. NAME OF FASTFOOD CHAIN INTHE PHILIPPINES
_______ 6. NUMBER OF CLASS PERIOD PER DAY
_______ 7.TIME REQUIRED SOLVING MATHEMATICS PROBLEMS
_______8. MONTHLY AMOUNT OF GASOLINE USED BYTHE FAMILY
_______9. FAVORITE COFFEE SHOP.
_______10. NUMBER OF SETS OF UNIFORM OWNED.

25. A market research is being conducted on internet usage of
students in grade 11.The following were included in the survey:
1. Gender
2. Type of school currently enrolled in (public or private).
3. Name of Internet provider
4. Type of internet service availed (1 for pre-paid, 2 for post-paid).
5. Approximate amount spent monthly on internet service

26. A market research is being conducted on internet usage of students in
grade 11.The following were included in the survey:
6.You pay the internet services through.
7. Number of emails received in a week.
8. Numbers of hours you surf the internet.
9. Rank the following activities being done using the internet (doing
research, playing games, downloading music or movies, chatting)
according to frequency; 1 being the most frequent.
10. Degree of satisfaction with the internet service provider with 1 as the
least satisfied and 6 is the most satisfied.

27. FOR EACH QUESTION:
Item
No.
CLASSIFICATION
1
2
3
4
5
6
7
8
9
10
A. LISTTHE DATATHAT COULD BE COLLECTED (MAXIMUM OFTHREE DATA FOR EACH QUESTION
B. CLASSIFYTHE DATA ACCORDING TO NATURE
C. IFTHE DATA IS MEASURED, IDENTIFY ITS SCALE, AND JUSTIFYYOUR ANSWER

28. EXERCISES:
B. FOR EACH STATEMENT, DECIDEWHETHER DESCRIPTIVE
OR INFERENTIAL STATISTICS IS USED.
___________1.The average life expectancy at birth in the Philippines for 2014 is 72.48
years. (Source: www.indexmundi.com).
___________ 2.Taking slimming pills will help you lose weight.
___________ 3.The total amount of estimated losses from typhoon Ondoy is ₱11B.
(source:www.rappler.com)
____________4.The studies show that gender is related to excellence in Mathematics.
(For example, if you are a boy, you excel in Mathematics).
____________ 5. In 2016, the government projects predicted that some 1.2 to 1.6
million students will enter the Senior High School.

29. EXERCISES:
C. DETERMINE WHETHERTHE STATEMENT IS QUALITATIVE (QL) OR
QUANTITATIVE (QN). WRITE QL OR QN ONTHE SPACE PROVIDED.
____1. In the Philippines, most of the high school graduates took education as a
course.
____ 2. The minimum wage of a contractual employee in Philippines is ₱13, 000.00.
_____3. It took 1 hour for Daisy to arrive to her work from her house.
_____4.The children in the daycare center were classified into infant, toddler, and
Pre-school.
_____ 5. Jamie wants to know the marital status of the faculty members in a large
University.

30. EXERCISES:
D. CLASSIFY EACHVARIABLE AS DISCRETE (D) OR CONTINUOUS (C).
WRITETHE LETTER D OR C INTHE SPACE PROVIDED.
____1.The lifetime of a calculator battery is 10 years.
____ 2. A hamburger stand solds 50 to 100 cheeseburgers near the
campus each day.
____3. A PhilippineTarsier weighs between 2.8 and 5.8 ounces.
____4. It takes Ms. Perez 1 hour to drive from her home to work.
____ 5. It 30 minutes for Mikka to answer mathematics word
problem.

32. GROUP WORK: (4 STUDENTS PER GROUP)

33. F. ANSWERTHE FOLLOWING QUESTIONS BASED ON
THE ARTICLES PROVIDED:
QUESTIONS:
1. Is the study experimental or observational?___________________________________________
2. What are the given variables in the study?____________________________________________
3. What are the qualitative data given in the study?______________________________________
4. Could it be concluded that the powerplant is safe to use by companies planning to use it (like
Aboitiz)?_________________________________________________________________________
5. Based on the Results of the study, what would you recommend to new companies or
establishments to save on expenses, especially on electricity consumption?
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________

34. ARTICLE 1:
ASEAGAS SEEKS REGULATORY NOD ON BIOMASS
PLANT’S GRID CONNECTION FACILITY
(BY MYRNA VELASCO, MANILA BULLETIN, OCTOBER 21, 2015 ISSUE)
Aboitiz firm Aseagas Corporation is seeking regulatory approval for a point-to point limited
transmission line that will connect 8.8 megawatt biomass power facility to the power grid.
It is emphasized in its filing with Energy Regulatory Commission (ERC) that it intends to
connect its power project via the 69 kilovolt (kV) Calaca-Nasugbu transmission line of the
National Grid Corporation of the Philippines.
The plant is targeted to kick-off with its commissioning phase within this month,
although the ERC is still scheduling public hearings on its petition.
The grid connection’s facility’s project cost will be ₱12.757 million according to the project
sponsor firm, with the bulked earmarked for supply of labor, materials and equipment.
“The construction of the Aseagas point-to-point project shall be funded internally and
externally from a pool of generated funds,” the Aboitiz firm said.

35. ARTICLE 1:
ASEAGAS SEEKS REGULATORY NOD ON BIOMASS
PLANT’S GRID CONNECTION FACILITY
(BY MYRNA VELASCO, MANILA BULLETIN, OCTOBER 21, 2015 ISSUE)
It added that it is “seeking to to undergo negotiations with the National Grid Corporation of the
Philippines (NGCP) as regards to the maintenance and operation of the dedicated point-to-point limited
transmission line.”
Aseagas has noted that based on the system impact study (SIS), undertaken for the project, the
planned point-to-point connection “is technically feasible.”
It added that “evaluation on the thermal loading of transmission line shows that there is no
overloading of existing lines that is directly linked to the interconnection of the project plant.”
Aseagas similarly indicated that “the plant can deliver its full capacity to the grid without
additional reinforcements needed to be set up by the NGCP.”
The biomass plant is being lined up to be among the renewable energy project that could avail of
the feed-in-tariff prescribed for that particular technology type.
The project was initially intended to produce “ liquid fuels,” but the collapse in global oil prices
reportedly prompted the project to shift into a power-producing venture.

36. F. ANSWERTHE FOLLOWING QUESTIONS BASED ON
THE ARTICLES PROVIDED:
QUESTIONS (ARTICLE 2):
1. Is the study experimental or observational?___________________________________________
2. What are the given variables in the study?____________________________________________
3. What are the qualitative data given in the study?______________________________________
4. Could it be concluded that the technology is not of a big help when it comes to productivity?
_________________________________________________________________________________
5. Based on the Results of the study, what would you recommend to new companies or
establishments to increase or improve labor or business productivity?
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________

37. ARTICLE 2:
THE LATEST RESEARCH ON LOW PRODUCTIVITY SAYS
TECHNOLOGY HASN’T HELPED MUCH
(BY GREGG ROBB,WWW.MARKETWATCH.COM, MARCH 4, 2016 ISSUE)
WASHINGTON (MarketWatch) — A key indicator of the long-term vibrancy of the
economy, labor productivity, is not weak because of inaccurate government statistics or a failure
to account for the rise of Google, Facebook and the Internet, according to new research from a
team of Federal Reserve economists.
U.S. productivity, or output per hour of labor, has been weak over the past decade, rising
a meager 0.7% for all of 2015.This is down from the 2.7% seen after WorldWar II and through the
mid-1970s and 3% during the tech-boom of the mid-1990s through 2005.
All things equal, slower productivity means slower growth and living standards.
For years, economists have been debating the causes and even the accuracy of the
slowdown in productivity.
One common explanation from skeptics is that government statistics don’t capture
recent innovations like Google, Facebook or the Internet.

38. ARTICLE 2:
THE LATEST RESEARCH ON LOW PRODUCTIVITY SAYS
TECHNOLOGY HASN’T HELPED MUCH
(BY GREGG ROBB,WWW.MARKETWATCH.COM, MARCH 4, 2016 ISSUE)
But in research published Friday for a conference next week at the Brookings Institution, David
Byrne, an economist at the Fed, John Femald, an economist at the San Francisco Fed, and Marshall
Reinsdorf of the International Monetary Fund, argue that Google and Facebook are more akin to
television and what people do in their free time. So these developments don’t impact business
productivity all that much.
The researchers said that there could be another wave of the information technology
revolution from cloud computing, the Internet of things, and the radical increase in mobility
represented by smartphones.
“But since the early 1970s, modest and incremental productivity growth has more often been
the norm,” the paper concluded.
The researchers said they experimented with new measures for computers and
communications equipment that the government doesn’t use. On balance, using these
measurements, the labor productivity slowdown is modestly larger.

39. GENERALIZATION:
Define what is
statistics
Understand statistics
key concepts
Determine the
essential processes
involve in doing
statistics
Identify data and to
classify them
Use appropriate scales
of data measurement

40. END OF LESSON 1
Thank you.