I. INTRODUCCIÓN:
1.1. Problema:
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).
(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:
Figure 3.3 Broad Classification of Variables
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
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
pesos) Quantitative Discrete
Usual Daily Food Expenditure in
School (in pesos) Quantitative Discrete
Usual Number of Text Messages
Sent in a Day Quantitative Discrete
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. ASSESSMENT
Note: Answers are provided inside the parentheses and italicized.
1. 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
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)
b. 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)
c. Give at least two populations that could be observed from the variables identified in (b).
(Possible answer: The population is the set of all values of the highest educational attainment and another population is {single, married, divorced, separated, widow/widower})
2. 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)
3. A survey of students in a certain school is conducted. The survey questionnaire details the information on the following variables. For each of these variables, identify whether the variable is qualitative or quantitative, and if the latter, state whether it is discrete or continuous.
a. number of family members who are working (quantitative: discrete) b. ownership of a cell phone among family members (qualitative)
c. length (in minutes) of longest call made on each cell phone owned per month (quantitative: continuous)
d. ownership/rental of dwelling (qualitative)
e. amount spent in pesos on food in one week (quantitative: discrete) f. occupation of household head (qualitative)
g. total family income (quantitative: discrete)
h. number of years of schooling of each family member (quantitative: discrete) i. access of family members to social media (qualitative)
j. amount of time last week spent by each family member using the internet (quantitative: continuous)
Explanatory Note:
• Teachers have the option to just ask this assessment orally to the entire class, or to group students and ask them to identify answers, or to give this as homework, or to use some questions/items here for a chapter examination.