Lesson 3: Basic Terms in Statistics

TIME FRAME:1 hour session

OVERVIEW OF 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.

LEARNING OUTCOME(S): At the end of the lesson, the learner is able to

• 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);

LESSON OUTLINE:
1. Recall previous lesson on ‘Contextualizing Data’
2. Definition of Basic Terms in Statistics (universe, variable, population and sample)
3. Broad of Classification of Variables(qualitative and quantitative, discrete and continuous)

DEVELOPMENT OF THE LESSON

A. Recall previous lesson on ‘Contextualizing Data’
Begin by recalling with the students the data they provided in the previous lesson and how
they contextualized such data. You could show them the compiled data set in a table like this:
Number Usual Usual Daily Usual
of Age of Daily food number
Class Sex Height Most Usual Happiness
siblings Weight mother allowance expenditure of text
Student (in Preferred Sleeping Index for
(in (in kg) (in in school in school messages
Number cm) Color Time the Day
person) years) (in pesos) (in pesos) sent in a
day
1 M 2 60 156 60 200 150 20 RED 23:00 8
2 F 5 63 160 66 300 200 25 PINK 22:00 9
3 F 3 65 165 59 250 50 15 BLUE 20:00 7
4 M 1 55 160 55 200 100 30 BLACK 19:00 6
5 M 0 65 167 45 350 300 35 BLUE 20:00 8
: : : : : : : : : : : :
: : : : : : : : : : : :
Recall also their response on the first Ws of the data, that is, on the question “Who provided
the data?” We said last time the students of the class provided the data or the data were taken
from the students.
Another Ws of the data is What? What are the information from the respondents? and What
is the unit of measurement used for each of the information (if there are any)? Our responses
are the following:

• 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.

• 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.

B. Main Lesson

1. Definition of Basic Terms

The collection of respondents from whom one obtain the data is called the universe of the
study. In our illustration, the set of students of this Statistics and Probability class is our
universe. 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. So formally, we define universe as the collection or set of units or
entities from whom we got the data. Thus, this set of units answers the first Ws of data
contextualization.
On the other hand, the information gathered are referred to as the variables of the study and
in the data collection activity, we have 12 variables including Class Student Number. A
variable is a characteristic that is observable or measurable in every unit of the universe.
From each student of the class, we got the his/her 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. Since these characteristics are observable in each and every
student of the class, then these are referred to as variables.
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.
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.

We can further visualize these terms in the following figure:

VARIABLE 1 VARIABLE 2 VARIABLE 12

Unit!1! Value!1! Value!1! Value!1!

Unit!2! Value!2! Value!2! Value!2!
Unit!3! Value!3! Value!3! Value!3!
…..!
:! :! :! :!
:! :! :! :!
Unit!N! Value!N! Value!N! Value!N!
! !

UNIVERSE POPULATION POPULATION POPULATION OF

OF VARIABLE 1 OF VARIABLE 2 VARIABLE 12

Unit!1! Value!1!
:! :!
:! :!
Unit!n! Value!n!
SAMPLE
OR!

A SAMPLE OF UNITS A SAMPLE OF

POPULATION VALUES
Figure 3.1 Visualization of the relationship among universe, variable, population and sample.

2. Broad Classification of Variables

Following up with the concept of variable, inform the students that usually, 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 quantitative or qualitative, with the latter further
classified into discrete and continuous types (see Figure 3.3 below).
 Figure 3.3 Broad Classification of Variables

(i) 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).
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.

(ii) 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. Quantitative data may be further classified into:

a. 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.

b. 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.
With this classification, let us then test the understanding of our students by asking them to
classify the variables, we had in our last data gathering activity. They should be able to
classify these variables as to qualitative or quantitative and further more as to discrete or
continuous. If they did it right, you have the following:

VARIABLE TYPE OF TYPE OF

VARIABLE QUANTITATIVE
 VARIABLE
Class Student Number Qualitative
Sex Qualitative
Number of Siblings Quantitative Discrete
Weight (in kilograms) Quantitative Continuous
Height (in centimeters) Quantitative Continuous
Age of Mother Quantitative Discrete
Usual Daily Allowance in School (in Quantitative
Discrete
pesos)
Usual Daily Food Expenditure in School Quantitative
Discrete
(in pesos)
Usual Number of Text Messages Sent in Quantitative
Discrete
a Day
Usual Sleeping Time Qualitative
Most Preferred Color Qualitative
Happiness Index for the Day Qualitative

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.

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.

REFERENCES
Albert, J. R. G. (2008). Basic Statistics for the Tertiary Level (ed. Roberto Padua,
WelfredoPatungan, Nelia Marquez), published by Rex Bookstore.
Handbook of Statistics 1 (1st and 2nd Edition), Authored by the Faculty of the Institute of
Statistics, UP Los Baños, College Laguna 4031
Takahashi, S. (2009). The Manga Guide to Statistics. Trend-Pro Co. Ltd.

Workbooks in Statistics 1 (From 1st to 13th Edition), Authored by the Faculty of the Institute
of Statistics, UP Los Baños, College Laguna 4031