3. STATISTICS
Statistics is a branch of Mathematics
that deals with the collection,
organization, presentation, analysis,
and interpretation of data.
4. Statistics involves much more than simply drawing graphs
and computing averages.
• In education, it is frequently used to described test results.
• In science, the data resulting from experiments must be
collected and analyzed. Diseases are controlled through
analysis designed to anticipate epidemics. The lifetime of
a battery can be tested in a laboratory. Endangered
species of birds and other wildlife are protected through
regulations that react to statistical estimates.
5. Statistics involves much more than simply drawing graphs
and computing averages.
• Manufacturers can provide better product 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 become more critical in
your analysis of information; hence, you will not be misled
by the manufactured polls, graphs, and averages.
6. POPULATION &
SAMPLE
A population is a complete collection of all
elements (scores, people,...) to be studied.
A sample is a subcollection of elements
drawn from a population.
A census is collection data from every
element in a population.
7. POPULATION & SAMPLE
A researcher would like to conduct a survey to the 100
randomly chosen Grade 7 students of Benigno “Ninoy” S.
Aquino High School regarding the effect of blended
modality implemented in the fourth quarter.
POPULATION
Students of Benigno “Ninoy” S. Aquino High School
SAMPLE
100 randomly chosen Grade 7 Students
8. Identify the population and sample in each of the
following situation:
1.) A scientist is investigating the effectiveness of a new drug to
relieve the symptoms of hypertension. He administers the drug to
100 adults.
2.) A survey will be given to 50 students randomly selected from
the senior class at GEOM High School.
3.) A mayor selected 250 voters to see if the people in his town
thought he was delivering good services.
4.) A vaccine was given to 10 randomly chosen senior Makatizen.
9. TYPES OF SAMPLE
1.) In a random sample, each
member of the population has
an equally likely chance of
being selected. The members
of the sample are chosen
independently of one another.
10. TYPES OF SAMPLE
2.) A convenience sample
is a sample that is chosen
because of its convenient
proximity and accessibility
to the researcher.
11. TYPES OF SAMPLE
3.) In a stratified random sample,
the population is divided into
subgroups, so that each
population members is in only
one subgroup. In here,
individuals are chosen randomly
from each subgroup.
12. TYPES OF SAMPLE
4.) A cluster sample is a
sample that consists of items
in a group such as a
neighborhood or a household.
The group ,ay be chosen at
random.
13. TYPES OF SAMPLE
5.) A systematic sample is
obtained using an ordered
list of the population, thus
selecting members
systematically from the list.
14. Identify which type of sampling is used: random,
stratified, cluster, systematic or convenience.
Situation: Mr. Belleza plans to choose four students from
the Math Club to be in s publicity photo. How could he
choose the four students?
1.) Mr. Belleza could put the names of all the students in a
box, picking the names without looking.
2.) Mr. Belleza could choose the first student in row 1, the
second in row 2, the third in row 3, and so on.
15. 3.) Mr. Belleza could choose the four students in the fourth
row.
4.) Mr. Belleza could choose a group of four students in
the corner of the last row.
5.) Mr. Belleza could mix the names of the boys and
choose two from the group. He does the same for the
girls.
16. NATURE OF DATA
Data are raw material which the statistician works.
These are collection of values in a particular
variable
Quantitative Data - consist of numbers representing
counts or measurements.
Qualitative Data - can be separated into different
categories that are distinguished by some nonnumeric
characteristics.
17. Classify the following as either quantitative or
qualitative.
1.) Opinion on a political issue
2.) Number of hospitals that has a nuclear center
3.) Ages of Congressmen
4.) Trending hair color
5.) religion
18. CLASSIFICATION OF QUANTITATIVE
DATA
Discrete data result from either a finite number of
possible values or countable number of possible values
as 0, or 1, or 2, and so on. (Can be obtained by
counting.)
Continuous data result from infinitely many possible vales
that can be associated with points on a continuous scale in
such a way that there are no gaps or interruptions. (Can be
obtained by measuring.)
20. NOMINAL LEVEL
• Categorical data and numbers that are simply
used as identifiers.
• Classifies data into names, labels or
categories in which no order or ranking can be
imposed.
Examples:
1. gender. categorized as male or female.
2. jersey number. the jersey number is only used to identify
the player.
3. id number. the id number is used to assign the identity of
an individual in a certain school/university.
21. ORDINAL LEVEL
• Classifies data into categories that can be
ordered or ranked, but precise differences
between the ranks do not exist.
Examples:
22. INTERVAL LEVEL
• Have a precise difference between measures but the
zero value is arbitrary and does not imply an absence
of the characteristic being measured.
Example:
Temperature- If the temperature falls at
zero degrees, it does not imply that
there is no temperature in an area still
zero indicates a measure.
23. RATIO LEVEL
• Based on a standard scale which have a fixed
zero point in which the zero value denotes the
complete absence of the characteristic being
measured.
Example:
Money - if a person declared that
he has only php 0 on his pocket,
it simply implies that the person
has no money at all.
24. Let us take an example of a “100-meter race” in a tournament where three runners are
participating from three different regions of the Philippines.
Each runner is assigned a number (displayed in uniform) to differentiate from each
other. The number displayed in the uniform to identify runners is an example of
nominal scale.
Once the race is over, the winner is declared along with the declaration of first runner up and second
runner up based on the criteria that who reaches the destination first, second and last. The rank order
of runners such as “second runner up as 3”, “first runner up as 2” and the “winner as 1” is an example
of ordinal scale.
During the tournament, judge is asked to rate each runner on the scale of 1–10 based on certain
criteria. The rating given by the judge is an example of interval scale.
The time spent by each runner in completing the race is an example of ratio scale.
25. Determine which level of measurements (nominal,
ordinal, interval, ratio) is used:
1.) average annual temperature in Tagaytay
2.) weights of garbage discarded by households
3.) a judge rates some presentations as “good”
4.) the political party to which each governor belongs
5.) volume of water being wasted
