Meaning and Importance of Statistics

Lesson 1
MEANING AND IMPORTANCE
OF STATISTICS

OBJECTIVES:
After the successful discussion in class, you
will be able to:
 Define statistics and discuss the history of
statistics;
 Understand the terms related to statistics;
and
 Differentiate the two branches of
Statistics.

STATISTICS
 It is imperative that every Filipino student
have a clear understanding of the nature
and definition of Statistics as a field of
discipline. However, understanding the
nature of statistics requires the students to
go beyond its definition and appreciate its
application.

Definitions of Statistics
 Plural Sense: Statistics pertains to
numerical data or figures that can be
presented and counted out of observations
done by individual.
 Singular Sense: Statistics is a branch of
science that deals with the collection,
tabulation and presentation. Analysis and
interpretation of the data that can be used
when making decisions in the face of
uncertainty.

HISTORY OF STATISTICS
 Simple forms of statistics have been used
to record numbers of people, animals, and
inanimate objects on skins, slabs, or sticks
of wood and the walls of caves.
 Before 3000 B.C., Babylonians small clay
tablets
 The Egyptians analyzed the population
and material wealth of their country before
building a pyramid.

 Aside from secular records, Statistics could be
seen in Biblical accounts such as the one
recorded in numbers 31:25-41 when, during the
times of Moses, statistics were gathered for
purposes such as taxation, military service and
priestly duties.
 Statistics has evolved from the word “Statistik”
which was popularized by a German political
scientist Gottfried Achenwall. The word was
derived from Latin word “Status” or the Italian
word “Statista” which means “State”. Its English
use was introduced early in the 19th Century by
Sir John Sinclair to mean “the collection and
classification of data”.

SIGNIFICANCE OF STATISTICS
 Good decisions are driven by data. Proper
evaluation and interpretation of these data
could be useful in making the best decision
for practicality every facet of man’s daily
activities.

Significance of Statistics in the ff. areas:
 Society
 Business and Industry
 Transportation Safety
 Peace and Order
 Sports
 Consumers
 Health
 Agriculture

AREAS OF STATISTICS
 Descriptive Statistics
 Is the discipline of quantitatively describing main features
of a collection of data without drawing conclusions about
a large group. Descriptive statistics can be thought of as
a straightforward presentation of facts.

 Inferential Statistics
 Concerned with the analysis of a subset of data or
sample leading to predictions or inferences about the
entire set of data or population. Some examples shows
the analysis of the samples are generalized for the large
population that the sample represents.

Figure 1.1
Age-Sex Population Pyramid
Philippines: 2010

Meaning and Importance of Statistics

Lesson 2
TERMS AND SYMBOLS USED IN
STATISTICS

OBJECTIVES:
After the successful discussion in class, you
will be able to:
 Understand the terms related to statistics;
 Identify the different categories and types
of variables;
 Differentiate population from a sample;
 Distinguish parametric test from non-
parametric test; and
 Familiarize the different statistical symbols
used in this book.

VARIABLES
 Figures or any characteristics, numbers, or
quantity that can be measured or counted
and varies over time and on different
individual or object under consideration.
Arrows are used to illustrate relationships
among variables.

Types of variables
 1. Independent Variable – experimental
or predictor
 2. Dependent Variable – outcome that is
presumed effect
 3. Extraneous Variables – interferes or
interacts with IV

Classification of Variables
 Can be categorize according to the manner of measurement
and presentation.

 1. Qualitative Variable – categorical variable. It describes the
qualities or characteristics of the samples

 2. Quantitative Variable – give numerical responses
representing an amount or number of something.

 3. Discrete Quantitative Variable – countable variable. It
assumes fixed or countable values of something being
measured.

 4. Continuous Quantitative Variable –non countable
variable. It cannot take on finite values but the values are
associated with points on an interval of the real line.

Kinds of Variables
VARIABLES
QUANTITATIVE
DISCRETE CONTINUOUS
QUALITATIVE

STATISTICAL TERMS
 Measurement – is the process done by
individual to determine the value or label of
the variable based on what has been
observed.
 Observation – is defined as the realized
value of the variable
 Population – is the collection of things or
observational units under consideration. It
is an aggregate set of individuals with
varied characteristics and could be classify
according to age and sex.

Three (3) Factors Influencing Population
 1. Fertility – this pertains to the birth rate
in a community
 2. Mortality – this is the death rate in a
community
 3. Migration – this is the number of people
moving in and out of a community.
 The Statistical Population is the set of
all possible values of the variable.

 POPULATION– changes in population and its
structure significantly affects policy making and the
development of a certain community.
 SAMPLE – commonly defined as the subset of
population that shares the same characteristics of
the population
 SAMPLING – process of selecting a part or subset
of a population. You can use your sample to make
inferences for your population.

Common Reasons for Sampling
 Limited budget, time constraints, lack of manpower,
accessibility, peace and order of the area, size of the
population, and availability and cost of the
experimental materials.

Types of Sampling Techniques
 Probability Sampling
It is the one in which each sample has the
same probability of being chosen.
 Non-Probability Sampling
In this type of population sampling, members of
the population do not have equal chance of
being selected.
 No rule sampling
We take sample without any rule

Types of Probability Sampling
 Random Sampling
 Systematic Sampling
 Stratified Sampling
 A. Proportionate Stratified Random
Sampling
 B. Disproportionate Stratified Random
Sampling
 Cluster Sampling

Types of Non-Probability Sampling
 Convenience Sampling
 Sequential Sampling
 Quota Sampling
 Judgmental/ Purposive Sampling
 Snowball Sampling

 Information is limited to useful facts that an analyst or a
decision maker can use in solving problems.

 Parameter is a set of numerical figures describing the
characteristic of the population.

 Data mining is simply the process of examining or going to
the details of the data. Important details are carefully studied
and scrutinized.

 Sex is the biological description of a person either a male or a
female.

 Operational Definition is how you define the word/s
according to its use and purpose.

KINDS OF STATISTICAL TEST
 1. PARAMETRIC TEST
 Requires normality of the distribution and the
levels of measurement should be either interval
or ratio. The observations must be independent
and the populations must have the same
variances.
 It implies that parametric tests are more efficient
than its non-parametric tests counterpart
 Parametric tests are more appropriate when
sample sizes are small.

KINDS OF PARAMETRIC TEST
 1. T-test
 2. Z-test
 3. F-test
 4. Analysis of Variance
 5. Pearson Product Moment Coefficient of
Correlation
 6. Simple Linear Regression
 7. Multiple Regression Analysis

 2. NON-PARAMETRIC TEST
 Does not require normality of the
distribution and the levels of measurement
must be either interval ordinal.

STATISTICAL SYMBOLS
 ∑
 N Xm
 n i
 F X
 <F Md
 >F X
 Cs Y
 SD R
 S² R²
 CD

Lesson 3
LEVELS OF MEASUREMENT

OBJECTIVES:
After the successful discussion in class, you will be
able to:
 Define and distinguish nominal, ordinal,
interval, and ratio scales;
 Enumerate the limitations of each scale;
 Apply measurement scales in choosing
statistical tools; and
 Give examples of errors that can be made by
having inadequate understanding on the proper
use of measurement scales.

 Variables are considered the substance of statistics.
Before we can conduct statistical investigation and
analysis, we need first to fully understand the nature
and measurements of the variables to be studied.
 The in-depth understanding of your variables may
result to correct and usable inferences or
conclusions.
 When we choose our statistical tools to be used in
studying our variables, we need to consider the four
measurement scales. For parametric test, the
measurement scales should be either interval or
ratio, and for non-parametric test, the
measurement scales should be either nominal or
ordinal.

FOUR LEVELS OF MEASUREMENT
SCALES
 NOMINAL LEVEL
 ORDINAL LEVEL
 INTERVAL LEVEL
 RATIO LEVEL

Lesson 4
Data Collection and
Presentation

Data Collection Presentation
 Data can be defined as groups of
information that represent the qualitative or
quantitative attributes of a variable or set of
variables, which is the same as saying that
data can be any set of information that
describes a given entry. Data in statistics
can be classified into grouped data and
ungrouped data.

Ungrouped Data
 Any data that you first gathered and is the
data in the raw. An example of ungrouped
data is any list of numbers that you can
think of.
 Example:
 The marks obtained by 20 students in
class in a certain examination are given
below:
 21, 23, 19, 17, 12, 15, 15, 17, 17, 19, 23,
23, 21, 23, 25, 25, 21, 19, 19, 19

Array
 An arrangement of ungrouped data in
ascending or descending order of
magnitude is called an array.
 Example:
 The marks obtained by 20 students in
class in a certain examination are given
below:
 21, 23, 19, 17, 12, 15, 15, 17, 17, 19, 23,
23, 21, 23, 25, 25, 21, 19, 19, 19
 (Arrange the scores in ascending order)

Frequency Distribution Table or
Frequency Chart
 A frequency is the number of times a data
value occurs. For example, if ten students
score 80 in Statistics, then the score of 80
has a frequency of 10. Frequency is often
represented by letter f.
 A Frequency Chart is made by arranging
data values in ascending order of
magnitude along with their frequencies.

Example:
 We take each observation from the data, one at a time,
and indicate the frequency (the number of times the
observation has occurred in the data) by small line, called
tally marks. For convenience we write tally marks in
bunches of five, the fifth one crossing the fourth
diagonally. In the table so formed, the sum of all the
frequency is equal to the total number of observations in
the given data.
Marks Tally Marks Frequency

Grouped Data
 Is data that has been organized into
groups known as classes.
 Grouped data has been ‘classified’ and
thus some level of data analysis has taken
place, which means that the data is no
longer raw.

 When the set of data values are spread out, it is
difficult to set up a frequency table for every data
value as there will be too many rows table. So
we group the data into class intervals (or
groups) to help us organize, interpret and
analyze the data.
 Each class is bounded by two figures, which are
called class limits. The figure on the left side of
a class is called its lower limit and that on its
right is called its upper limit.
 Ideally, we should have between five and ten
rows in a frequency table. Bear this in mind when
deciding the size of the class interval (or group).

TYPES OF GROUPED FREQUENCY
DISTRIBUTION
 1. Exclusive form (or Continuous Interval
Form): A frequency distribution in which the
upper limit of each class is excluded and lower
limit is included is called an exclusive form.

 2. Inclusive Form (or Discontinuous
Interval Form): A frequency distribution in
which upper limit as well as lower limit is
included is called an inclusive form.

Calculating Class Interval
 Given a set of raw or ungrouped data, how
would you group that data into suitable
classes that are easy to work with and at
the same time meaningful?
 The first step is to determine how many
classes you want to have. Next, you
subtract the lowest value in the data set
from the highest value in the data set and
then you divide by the number of classes
that you want to have.

The general rules for constructing a
frequency distribution are:
 There should not be too few or too many classes
 Insofar as possible, equal class intervals are
preferred. But the first and last classes can be
open-ended to cater for extreme values.
 Each class should have a class mark to
represent the classes. It is also named as the
class midpoint of the ith class. It can be found by
taking simple average of the class boundaries or
the class limits of the same class.

Example:
 Group the following raw data into ten
classes.
 An array of the marks of 25 students in
ascending order.
 8, 10, 11, 12, 14, 16, 16, 16, 20, 24, 25, 25,
25, 29, 30, 33, 35, 36, 37, 40, 40, 42, 45,
45, 48.

GRAPHICAL METHODS
 Frequency distributions and are usually illustrated
graphically by plotting various types of graphs:
1. Bar Graph - A bar graph
is a way of summarizing a
set of categorical data. It
displays the data using a
number of rectangles, of the
same width, each of which
represents a particular
category. Bar graphs can be
displayed horizontally or
vertically and they are
usually drawn with gap
between the bars

GRAPHICAL METHODS
2. Histogram - A
histogram is a way of
summarizing data that
are measured on an
interval scale (either
discrete or continuous). It
is often used in
exploratory data analysis
to illustrate the features
of the distribution of the
data in a convenient
form.

GRAPHICAL METHODS
3. Pie Chart - A pie chart is used to display a set
of categorical data. It is a circle, which is divided
into segments. Each segment represents a
particular category. The area of each segment is
proportional to the number of cases in that
category.

GRAPHICAL METHODS
4. Line Graph - A line graph is particularly useful
when we want to show the trend of a variable
over time. Time is displayed on the horizontal axis
(x-axis) and the variable is displayed on the
vertical axis (y-axis).

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