As continuation of Lesson 2 (where we contextualize data) in this lesson we define basic terms in statistics as we continue to explore data. These basic terms include the universe, variable, population and sample. In detail we will discuss other concepts in relation to a variable.

1. BASIC TERMS
IN
STATISTICS

2. OVERVIEW OF THE LESSON
As continuation of Lesson 2 (where we
contextualize data) in this lesson we
define basic terms in statistics as we
continue to explore data. These basic
terms include the universe, variable,
population and sample. In detail we will
discuss other concepts in relation to a
variable.

3. LEARNING OUTCOMES
•Define universe and differentiate it
with population; and
•Define and differentiate between
qualitative and quantitative variables,
and between discrete and continuous
variables (that are quantitative);

4. [CONSOLIDATED
DATA]

5. RECALL
1. Who provided the data?
•The students in this class provided
the data.

6. WHAT? WHAT ARE THE INFORMATION
FROM THE RESPONDENTS?
• The information gathered include Class
Student Number, Sex, Number of
Siblings, Weight, Height, Age of Mother,
Usual Daily Allowance in School, Usual
Daily Food Expenditure in School,
Usual Number of Text Messages Sent in
a Day, Most Preferred Color, Usual
Sleeping Time and Happiness Index for
the Day.

7. WHAT? WHAT IS THE UNIT OF
MEASUREMENT USED FOR EACH OF THE
INFORMATION (IF THERE ARE ANY)?
• The units of measurement for the
information on Number of Siblings,
Weight, Height, Age of Mother, Usual
Daily Allowance in School, Usual Daily
Food Expenditure in School, and Usual
Number of Text Messages Sent in a Day
are person, kilogram, centimeter, year,
pesos, pesos and message,
respectively

8. DEFINITION OF BASIC TERMS

9. UNIVERSE
• the collection or set of units or entities from
whom we got the data
• a universe is not necessarily composed of
people. Since there are studies where the
observations were taken from plants or
animals or even from non-living things like
buildings, vehicles, farms, etc.
• This set of units answers the first W’s of
data contextualization.

10. VARIABLE
• a characteristic that is observable or
measurable in every unit of the
universe
• the information that you were asked are
referred to as the variables of the study
and in the data collection activity, we have
12 variables including Class Student
Number

11. EXAMPLES OF VARIABLE FROM
THE ACTIVITY
• age, number of siblings, weight, height, age
of mother, usual daily allowance in school,
usual daily food expenditure in school,
usual number of text messages sent in a
day, most preferred color, usual sleeping
time and happiness index for the day.
• these characteristics are observable in each
and every student of the class, then these
are referred to as variables.

12. POPULATION
• The set of all possible values of a
variable is referred to as a population.
• Thus for each variable we observed, we
have a population of values. The number of
population in a study will be equal to the
number of variables observed.
• In the data collection activity we had, there
are 12 populations corresponding to 12
variables.

13. SAMPLE
• A subgroup of a universe or of a
population is a sample.
• There are several ways to take a sample
from a universe or a population and the
way we draw the sample dictates the kind
of analysis we do with our data.

15. BROAD CLASSIFICATION OF
VARIABLES

16. • A variable takes on several values. But
occasionally, a variable can only assume
one value, then it is called a constant. For
instance, in a class of fifteen-year olds, the
age in years of students is constant.
• Variables can be broadly classified as either
qualitative or quantitative, with the latter
further classified into discrete and
continuous types

18. QUALITATIVE
• variables express a categorical attribute,
such as sex (male or female), religion,
marital status, region of residence, highest
educational attainment.
• Qualitative variables do not strictly take on
numeric values (although we can have
numeric codes for them, e.g., for sex
variable, 1 and 2 may refer to male, and
female, respectively).

19. QUALITATIVE
• Qualitative data answer questions “what
kind.” Sometimes, there is a sense of
ordering in qualitative data, e.g., income data
grouped into high, middle and low-income
status. Data on sex or religion do not have
the sense of ordering, as there is no such
thing as a weaker or stronger sex, and a
better or worse religion.
• Qualitative variables are sometimes referred
to as categorical variables.

20. QUANTITATIVE
• (otherwise called numerical) data, whose
sizes are meaningful, answer questions
such as “how much” or “how many”.
Quantitative variables have actual units of
measure. Examples of quantitative
variables include the height, weight,
number of registered cars, household size,
and total household expenditures/income
of survey respondents.

21. CLASSIFICATIONS OF
QUANTITATIVE DATA

22. DISCRETE
• data are those data that can be counted,
e.g., the number of days for cellphones to
fail, the ages of survey respondents
measured to the nearest year, and the
number of patients in a hospital. These
data assume only (a finite or infinitely)
countable number of values.

23. CONTINUOUS
•data are those that can be
measured, e.g. the exact height of
a survey respondent and the
exact volume of some liquid
substance. The possible values
are uncountably infinite.

25. VARIABLE TYPE OF
VARIABLE
TYPE OF QUANTITATIVE
VARIABLE
CLASS STUDENT NUMBER
SEX
NUMBER OF SIBLINGS
WEIGHT
HEIGHT
AGE OF MOTHER
USUAL DAILY ALLOWANCE
USUAL DALY FOOD
EXPENDITURE
USUAL NUMBER OF TEXT
MESSAGES SENT
USUAL SLEEPING TIME
MOST PREFERRED COLOR
HAPPINESS INDEX
QUALITATIVE
QUALITATIVE
QUANTITATIVE
QUANTITATIVE
QUANTITATIVE
QUANTITATIVE
QUANTITATIVE
QUANTITATIVE
QUANTITATIVE
QUALITATIVE
QUALITATIVE
QUALITATIVE
DISCRETE
CONTINUOUS
CONTINUOUS
DISCRETE
DISCRETE
DISCRETE
DISCRETE

26. SPECIAL NOTE
For quantitative data, arithmetical operations have
some physical interpretation. One can add 301 and
302 if these have quantitative meanings, but if, these
numbers refer to room numbers, then adding these
numbers does not make any sense. Even though a
variable may take numerical values, it does not make
the corresponding variable quantitative! The issue is
whether performing arithmetical operations on these
data would make any sense. It would certainly not
make sense to sum two zip codes or multiply two
room numbers

27. KEY POINTS
• A universe is a collection of units from which the data were
gathered.
• A variable is a characteristic we observed or measured from
every element of the
universe.
• A population is a set of all possible values of a variable.
• A sample is a subgroup of a universe or a population.
• In a study there is only one universe but could have several
populations.
• Variables could be classified as qualitative or quantitative,
and the latter could be further
classified as discrete or continuous.

28. ASSESSMENT
1/4

29. A market researcher company requested all teachers of a
particular school to fill up a questionnaire in relation to
their product market study. The following are some of the
information supplied by the teachers:
• highest educational attainment
• predominant hair color
• body temperature
• civil status
• brand of laundry soap being used
• total household expenditures last month in pesos
• number of children in the household
• number of hours standing in queue while waiting to be served
by a bank teller
• amount spent on rice last week by the household
• distance travelled by the teacher in going to school
• time (in hours) consumed on Facebook on a particular day

30. a. If we are to consider the collection of information gathered
through the completed questionnaire, what is the universe
for this data set?
b. Which of the variables are qualitative? Which are
quantitative? Among the quantitative variables, classify
them further as discrete or continuous.
• highest educational attainment
• predominant hair color
• body temperature
• civil status
• brand of laundry soap being used
• total household expenditures last month in pesos
• number of children in a household
• number of hours standing in queue while waiting to be served
by a bank teller
• amount spent on rice last week by a household
• distance travelled by the teacher in going to school
• time (in hours) consumed on Facebook on a particular day

31. ANSWERS

32. A. IF WE ARE TO CONSIDER THE COLLECTION OF
INFORMATION GATHERED THROUGH THE COMPLETED
QUESTIONNAIRE, WHAT IS THE UNIVERSE FOR THIS DATA
SET?
(The universe is the set of all
teachers in that school)

33. WHICH OF THE VARIABLES ARE QUALITATIVE? WHICH ARE
QUANTITATIVE? AMONG THE QUANTITATIVE VARIABLES,
CLASSIFY THEM FURTHER AS DISCRETE OR CONTINUOUS.
• highest educational attainment (qualitative)
• predominant hair color (qualitative)
• body temperature (quantitative: continuous)
• civil status (qualitative)
• brand of laundry soap being used (qualitative)
• total household expenditures last month in pesos (quantitative: discrete)
• number of children in a household (quantitative: discrete)
• number of hours standing in queue while waiting to be served by a bank teller
(quantitative: discrete)
• amount spent on rice last week by a household (quantitative: discrete)
• distance travelled by the teacher in going to school (quantitative:
continuous)
• time (in hours) consumed on Facebook on a particular day(quantitative:
continuous

34. ASSIGNMENT

35. The Engineering Department of a big city did a listing
of all buildings in their locality. If you are planning to
gather the characteristics of these buildings,
a. what is the universe of this data collection activity?
b. what are the crucial variables to observe? It would
also be better if you could classify the variables as
to whether it is qualitative or quantitative.
Furthermore, classify the quantitative variable as
discrete or continuous.

36. ANSWERS

37. The Engineering Department of a big city did a listing of all
buildings in their locality. If you are planning to gather the
characteristics of these buildings,
a. what is the universe of this data collection activity?
(Set of all buildings in the big city)
b. what are the crucial variables to observe? It would also be
better if you could classify the variables as to whether it is
qualitative or quantitative. Furthermore, classify the
quantitative variable as discrete or continuous.
(A possible answer is the number of floors in the building,
quantitative, discrete)