Lesson
1
Basic Statistical Concepts
INTRODUCTION:
This lesson focuses on the basic concepts in of statistics including levels of
measurement. In measurement you will be learning the rules in assigning
numbers or symbols to the levels of our variables. Learning the different levels of
measurement will help you decide which statistical tool is appropriate in
analyzing the data.
OBJECTIVES:
At the end of this lesson, you should be able to:
1. Define the basic concepts of statistics;
2. Give examples of the different levels of measurement;
3. Differentiate:
a. Descriptive vs. inferential statistics
b. Data vs. variable
c. Population vs. sample
d. Parameter vs. statistics
Basic Concepts in Statistics
The word statistics is derived from the Greek word statistiks (Mariappan,
2019). The early use of statistics can be traced from the administration of the
state regarding the population and property usually for war and finance
purposes. Statistics is defined as the science of collection, organization,
presentation and analysis of data. Thus, one can draw conclusion and make
reasonable decision based on the analysis of that data.
Areas of Statistics
There are two broad areas of statistics- the descriptive and inferential.
Descriptive statistics can be defined as a set of methods involving the
collection, presentation and summarization by means of numerical descriptions.
Inferential statistics, on the other hand, is a set of methods that allow
estimation or testing of the characteristics of the population based only from the
sample drawn from that population.
Examples of Descriptive Statistics
1. The weekly mean sales of TV sets in a certain stores.
2. Alcohol is the most frequent disinfectant against COVID – 19.
3. At least 5% discount is deducted on the online sale.
4. The rice importation was doubled last year compare to the rice
importation two years ago.
5. The median age of the College of Business and Accountancy students is
25 years old.
Examples of Inferential Statistics
1. Salary predicts the life satisfaction of businessmen in Antique.
2. Productivity of crops is a factor in determining the choice of students to
go into farming.
3. Awareness of COVID – 19 symptoms is directly related to resiliency of the
residents living in Cebu City.
4. Number of received calls predicts the number of orders in a certain flower
shop.
Data is used to describe a collection of natural phenomena descriptors,
including the result of experience, observation or experiment. These could be
numbers, words or images that are used as measurement or result from
observations of a set of variables. Data can be drawn from the population or
sample. Population is the entirety of individuals or objects of interest. Sample
is a portion or part of the population of interest. The measures of the population
are called parameter and the measures of the sample are called statistics or
estimates. For example, during the 2020 census the mean age of Antiqueños
represents the parameter however if the researcher took sample from the entire
population of Antiqueños and then compute the mean age, the value is called
estimate. In other words, all values taken from the population is called the
parameter while values taken from the sample is called estimates.
Variable is the characteristics of an individual or object that can be
measured. A variable must vary or have different values in the study. For
example, sex is a variable because it can have two values, male and female.
However, if you are studying the quality of life of seamen in certain area and
they are all male, sex cannot be considered as a variable in that study.
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Scale of Measurement
There are four (4) scales of measurement – nominal, ordinal, interval and
ratio.
Nominal scale objects or individuals are assigned into categories and
have no numerical properties. This is the lowest scale. For examples, sex (male,
female), marital status (single, married), highest educational attainment
(elementary, secondary, or college graduate) and bath soap brand (Safeguard,
Palmolive, Zest, Bioderm, etc.) are nominal in nature. They do not possess
quantitative properties.
Ordinal scale objects or individuals form a category and the categories
form a rank along continuum. Ordinal data are sometimes referred to as ranked
data and they can be arranged in order either descending or ascending. Even
the data are ranked; their distances may not be equal. For example, the top
three performing students in a class are ranked as first, second and third. The
difference of scores between the first and the second may not be equal to the
difference between the scores of the second and third. Another example of
ranked data are academic rank (Instructor I, II, III, Asst. Instructor I, II, III,
etc.) and shoe size (small, medium, large).
Interval scale objects or individuals include the characteristics of ordinal
scale objects in addition to that the differences between the values is a constant
size. Another property of an interval scale measurement is that there is no
absolute zero. Meaning, zero does not denote the absence quantity being
measured. For example, temperature is an interval scale. The difference between
790C and 800C is equal to the difference between 80 0C and 810C. Furthermore,
00C does not denote absence of temperature.
Ratio scale objects or individuals has the characteristics than that of the
interval scale but an addition to that is that it has absolute zero. In ratio scale,
zero represents nothing. Zero means absence of the quantity being measured.
For example, weight, length, number of students inside the classroom or price of
commodities.
Type of Variables
There are two types of variables – qualitative and quantitative.
Qualitative Variables are variables that can be classified into
categories, according to characteristics or attributes. For example, sex is a
qualitative variable because you can classify as either male or female. Another
example is the color of the eyes (blue, brown, etc).
Quantitative variables are variables that are numerical or you can
possibly rank them. The example s of quantitative variables are age, number of
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deliveries, amount of sugar, etc. Quantitative variables can further be classified
discrete or continuous. Discrete variables can assume only certain values.
Usually, discrete variables are countable. Continuous variables are variables
that can assume any values between two values. For example, weight of cargo
vessels, time consumed in reading a novel and others.
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