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In its plural sense, statistics is a set of numerical data (e.g., vital statistics in a beauty contest,
monthly sales of a company, daily P-$ exchange rate).

In its singular sense, Statistics is that branch of science
presentation, analysis, and interpretation of data.

provides comparison
explains action that has taken place 
justifies a claim or assertion 
predicts future outcome
estimates unknown quantities

b.   Statistics summarizes data for public use

relationships worthy of further attention.

Example: A doctor can use Statistics to determine to what extent is an increase in

In the social sciences, it can guide and help researchers support theories and

models that cannot stand on rationale alone.
Example: Empirical studies are using Statistics to obtain socio-economic profile of

the middle class to form new socio-political theories on classes as the
existing theories apparently are no longer valid.

In business, a company can use statistics to forecast sales, design products, and

produce goods more efficiently.
Example: A pharmaceutical company can apply statistical procedures to find out if a

new formula is indeed more effective than the one being used. Results can
help the company decide whether to market the new formula or not.

In engineering, it can be used to test properties of various materials.

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Example:
A quality controller can use Statistics to estimate the average

lifetime of the products produced by their current equipment.

a.
Statistical Methods of Applied Statistics - refer to procedures and techniques used in the
collection, presentation, analysis, and interpretation of data.

Descriptive Statistics - methods concerned with the collection, description, and

analysis of a set of data without drawing conclusions or 
inferences about a larger set
the main concern is simply to describe the set of data such 
that otherwise obscure information is brought out clearly 
conclusions apply only to the data on hand

Inferential Statistics - methods concerned with making predictions or inferences

about a larger set of data using only the information gathered
from a subset of this larger set
the main concern is not merely to describe but actually
predict and make inferences based on the information
gathered
conclusions are applicable to a larger set of data which the
data on hand is only a subset

b. Statistical Theory of Mathematical Statistics - deals with the development and exposition

of theories that serve as bases of statistical methods.

Descriptive Statistics vs. Inferential Statistics

A bowler wants to find his bowling
average for the past 12 games.

A bowler wants to estimate his chance
of  winning  a  game  based  on  his
current
season
averages   and
the

A housewife wants to determine the
average weekly amount she spent on 
groceries in the past 3 months.

A housewife would like to predict
based on last year’s grocery bills, the
average weekly amount she will spend
on groceries for this year.
A politician would like to estimate,
based on an opinion poll, his chance
for winning in the upcoming election.

A politician wants to know the exact
number of votes he received in the 
last election.

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Definition.
A population is a collection of all the elements under consideration in a statistical
study.

A sample is a part or subset of the population from which the information is
collected.

Example:
A manufacturer of kerosene heaters wants to determine if customers are satisfied
with the performance of their heaters.
Toward this goal, 5,000 of his 200,000

customers are contacted and each is asked, “Are you satisfied with the performance
of the kerosene heater you purchased?” Identify the population and the sample for
this situation.

Definition.
A parameter is a numerical characteristic of the population.
A statistic is a numerical characteristic of the sample.

Example:
In order to estimate the true proportion of students at a certain college who smoke
cigarettes, the administration polled a sample of 200 students and determined that
the proportion of students from the sample who smoke cigarettes is 0.12.
the parameter and the statistic.

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Define the problem.
Formulate the research design. 
Collect the data.
Code and analyze the collected data. 
Interpret the results.

Definition.
A variable is a characteristic or attribute of persons or objects which can assume
different values or labels for different persons or objects under consideration.

Definition.
Measurement is the process of determining the value or label of a particular
variable for a particular experimental unit.

Definition.
An experimental unit is the individual or object on which a variable is measured.

Discrete variable
- a variable which can assume finite, or, at most,  countably

infinite number of values; usually
enumeration

Continuous variable - a  variable  which  can  assume

Qualitative variable - a variable that yields categorical

Quantitative variable- a variable that takes on numerical values representing an

amount or quantity (e.g., weight, height, no. of cars)

1.   Nominal Level (or Classificatory Scale)

The nominal level is the weakest level of measurement where numbers or symbols
are used simply for categorizing subjects into different groups.

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The ordinal level of measurement contains the properties of the nominal level, and in
addition, the numbers assigned to categories of any variable may be ranked or ordered 
in some low-to-high-manner.

The interval level is that which has the properties of the nominal and ordinal levels,
and in addition, the distances between any two numbers on the scale are of known
sizes. An interval scale must have a common and constant unit of measurement.
Furthermore, the unit of measurement is arbitrary and there is no “true zero” point.

The ratio level of measurement contains all the properties of the interval level, and in
addition, it has a “true zero” point.

Age (in years)
Number of correct answers in an exam

a.  Primary source    - data measured by the researcher/agency that published it

b.   Secondary source - any republication of data by another agency

Example: The publications of the National Statistics Office are primary sources

subsequent publications of other agencies are secondary sources.

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a.  Internal data
- information that relates to the operations and functions of the

b.   External data
- information  that relates to some activity outside the organization

Example: The sales data of SM is internal data for SM but external data for any other

1. Survey method
-
questions are asked to obtain information, either through
self-administered questionnaire or personal interview

Self-administered questionnaire
Personal interview

Obtained
information
is
limited
to
Missing    information
and
vague

subjects’ written answers to pre-arranged
questions
Lower response rate
It can be administered to a large number 
of people simultaneously
Respondents may feel freer to express

proper probing of the interviewer
Higher response rate through call-backs
It is administered to a person or group
one at a time
Respondent may feel more cautious

to answer
particularly
in
answering
sensitive

questions for fear of disapproval
It is more appropriate for obtaining
about complex emotionally-laden topics
or probing sentiments underlying an
expressed opinion

It  is  more  appropriate
objective information

2. Observation method
-
makes possible the recording of behavior but only at the
time  of  occurrence
(e.g.,  observing  reactions  to  a

does not rely on the respondent’s willingness to provide information

certain types of data can be collected only by observation (e.g. behavior

patterns of which the subject is not aware of or is ashamed to admit)

the potential bias caused by the interviewing process is reduced or

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things such as awareness, beliefs, feelings and preferences cannot be

the observed behavior patterns can be rare or too unpredictable thus

increasing the data collection costs and time requirements

3.
Experimental method  - a method  designed for collecting  data under controlled

conditions. An experiment is an operation where there is 
actual human interference with the conditions that can
affect the variable under study.
This is an excellent

method of collecting data for causation studies. If properly
designed and executed, experiments will reveal with a
good deal of accuracy, the effect of a change in one
variable on another variable.

Use of existing studies - e.g., census, health statistics, and weather bureau reports
4.

documentary  sources  -
published  or  written  reports,  periodicals,

field sources – researchers who have done studies on the area of interest

are asked personally or directly for information needed

5. Registration method  -
e.g., car registration, student registration, and hospital
admission

General Classification of Collecting Data

Definition.
Census or complete enumeration is the process of gathering information from
every unit in the population.

not always possible to get timely, accurate and economical data
costly, especially if the number of units in the population is too large

Definition.
Survey sampling is the process of obtaining information from the units in the
selected sample.

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Definition. A sampling procedure that gives every element of the population a (known) nonzero

chance of being selected in the sample is called probability sampling. Otherwise, 
the sampling procedure is called non-probability sampling.

Whenever possible, probability sampling is used because there is no

objective way  of  assessing  the reliability of  inferences under  non-probability 
sampling.

Definition. The target population is the population from which information is desired.

Definition. The sampled population is the collection of elements from which the sample is

Definition. The population frame is a listing of all the individual units in the population.

1. purposive sampling
-
sets out to make a sample agree with the profile of the
population based on some pre-selected characteristic

2. quota sampling
-
selects a specified number (quota) of
possessing certain characteristics

3. convenience sampling-
selects sampling units that come to hand or are convenient
to get information from

4. judgment sampling
-
selects sample in accordance with an expert’s judgment

Simple random sampling
Stratified random sampling 
Systematic sampling 
Cluster sampling
Multistage sampling
Sequential sampling  -
units are drawn one by one in a sequence without prior
fixing of the total number of observations and the results of

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the drawing at any stage are used to decide whether to
terminate sampling or not

Simple random sampling (SRS) is a method of selecting n units out of the N units in the
population in such a way that every distinct sample of size n has an equal chance of being
drawn. The process of selecting the sample must give an equal chance of selection to any
one of the remaining elements in the population at any one of the n draws.

Random sampling may be with replacement (SRSWR) or without replacement (SRSWOR).
In SRSWR, a chosen element is always replaced before the next selection is made, so that an 
element may be chosen more than once.

Make a list of the sampling units and number them from 1 to N.
Select n numbers from 1 to N using some random process, for example, the table of 
random numbers. n is distinct for SRSWOR , not necessarily distinct for SRSWR. 
The sample consists of the units corresponding to the selected random numbers.
Step 3:

The theory involved is much easier to understand than the theory behind other sampling
designs.
Inferential methods are simple and easy.

The sample chosen may be widely spread, thus entailing high transportation costs.
A population frame is needed.
SRS results in less precise estimates if the population is heterogeneous with respect to the 
characteristic under study.

In stratified random sampling, the population of N units is first divided into subpopulations
called strata. Then a simple random sample is drawn from each stratum, the selection being 
made independently in different strata.
Sample Selection Procedure

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Step 1: Divide the population into strata. Ideally, each stratum must consist of more or less

Step 2: After the population has been stratified, a simple random sample is selected from

Stratification may produce a gain  in precision  in the estimates  of characteristics  of the
population
It allows for more comprehensive data analysis since information is provided for each 
stratum.
It is administratively convenient.

A listing of the population for each stratum is needed.
The stratification of the population may require additional prior information about the 
population and its strata.

Systematic sampling with a “random start” is a method of selecting a sample by taking every
kth unit from an ordered population, the first unit being selected at random. Here k is called 
the sampling interval; the reciprocal 1/k is the sampling fraction.

Number the units of the population consecutively from 1 to N.
Determine k, the sampling interval using the formula k = N/n.
Select the random start r, where 1 < r < k. The unit corresponding to r is the first
unit of the sample.
The other units of the sample correspond to r + k, r + 2k, r + 3k, and so on.
Step 4:

Step 1: Number the units of the population consecutively from 1 to N.
Step 2: Let k be the nearest integer less than N/n.

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Step 3: Select the random start r, where 1

r
N. The unit corresponding to r is the first

Step 4: Consider the list of units of the population as a circular list, i.e., the last unit in the

list is followed by the first. The other units in the sample are the units corresponding 
to r + k, r + 2k, r + 3k,..., r+ (n-1)k.

It is easier draw the sample and often easier to execute without mistakes than simple random
sampling.
It is possible to select a sample in the field without a sampling frame. 
The systematic sample is spread evenly over the population.

If periodic regularities are found in the list, a systematic sample may consist only of similar
types. (Example: Store sales over seven days of the week – estimating total sales based on a 
systematic sample every Tuesday would be unwise.)
Knowledge of the structure of the population is necessary for its most effective use.

Cluster sampling is a method of sampling where a sample of distinct groups, or clusters, of
elements is selected and then a census of every element in the selected clusters is taken.
Similar to strata in stratified sampling, clusters are non-overlapping sub-populations which
together comprise the entire population. For example, a household is a cluster of individuals
living together or a city block might also be considered as a cluster. Unlike strata, however,
clusters are preferably formed with heterogeneous, rather than homogeneous elements so that
each cluster will be typical of the population.

Clusters may be of equal or unequal size. When all of the clusters are of the same size, the
number of elements in a cluster will be denoted by M while the number of clusters in the 
population will be denoted by N.

Number the clusters from 1 to N.
Select n numbers from 1 to N at random. The clusters corresponding to the selected 
numbers form the sample of clusters.
Observe all the elements in the sample of clusters.
Step 3:

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A population list of elements is not needed; only a population list of clusters is required.
Thus, listing cost is reduced. 
Transportation cost is also reduced.

The costs and problems of statistical analysis are greater.
Estimation procedures are more difficult.

In multistage sampling, the population is divided into a hierarchy of sampling units
corresponding to the different sampling stages. In the first stage of sampling, the population
is divided into primary stage units (PSU) then a sample of PSUs is drawn.
In the second

stage of sampling, each selected PSU is subdivided into second-stage units (SSU) then a
sample of SSUs is drawn.
The process of subsampling can be carried to a third stage, fourth

stage and so on, by sampling the subunits instead of enumerating them completely at each
stage.

Listing cost is reduced.
Transportation cost is also reduced.

Estimation procedure is difficult, especially when the primary stage units are not of the same
size.
Estimation procedure gets more complicated as the number of sampling stages increases. 
The sampling procedure entails much planning before selection is done.

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At last count, 38 airlines were operating Boeing 707’s, 720’s, and 727’s over the world’s

airlines.
The far-flung Boeing fleet has now logged an estimated 1,803,704,000 miles

(22,855,948,000 kms.) and has massed approximately 4,096,000 revenue flight hours.
Passenger totals stand at upwards of 71.6 million.

This presentation gives emphasis to significant figures and comparisons
It is simplest and most appropriate approach when there are only a few numbers to be 
presented

When a large mass of quantitative data are included in a text or paragraph, the presentation
becomes almost incomprehensible
Paragraphs can be tiresome to read especially if the same words are repeated so many times

the systematic organization of data in rows and columns

more concise than textual presentation
easier to understand
facilitates comparisons and analysis of relationship among different categories 
presents data in greater detail than a graph

1.   Heading
-
consists of a table number, title, and headnote. The title is a brief

statement of the nature, classification and time reference of the information presented
and the area to which the statistics refer.
The headnote is a statement enclosed in

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brackets between the table title and the top rule of the table that provides additional
title information.

2. Box Head
-
the portion of the table that contains the column heads which

describe the data in each column, together with the needed classifying and qualifying
spanner heads.

3.
Stub
-
the portion of the table usually comprising the first column on the

left, in which the stubhead and row captions, together with the needed classifying and
qualifying center head and subheads are located. The stubhead describes the stub
listing as a whole in terms of the classification presented.
The row caption is a

descriptive title of the data on the given line.

-
main part of the table; contains the substance or the figures of

5. Source note - an exact citation of the source of data presented in the table (should

always be placed when the figures are not original)

6.
Footnote
-
any statement or note inserted at the bottom of the table

Nonindex Crimes
44,065
71
37,365
59
38,002
58

Source Note
Source: Philippine National Police

The title should be concise, written in telegraphic style, not in complete sentence.

Table 4.4 – CRIME VOLUME AND RATE BY TYPE: 1991 – 1993

2,026
3           2,149        3        2,285           4

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Column labels should be precise. Stress differences rather than similarities between adjacent
columns. As much as possible, two or more adjacent columns should not begin nor end with 
the same phrase. This is frequently a signal that a spanner head is needed.
The arrangement of lines in the stub depends on the nature of classification, purpose of 
presentation or limitations of space.
Categories should not overlap.
The units of measure must be clearly stated.
Show any relevant total, subtotals, percentages, etc.
Indicate if the data were taken from another publication by including a source note.
Tables should be self-explanatory, although they may be accompanied by a paragraph that 
will provide an interpretation or direct attention to important figures.

a graph or chart is a device for showing numerical values or relationships in pictorial
form

main features and implications of a body of data can be grasped at a glance
can attract attention and hold the reader’s interest
simplifies concepts that would otherwise have been expressed in so many words 
can readily clarify data, frequently bring out hidden facts and relationships

1. Accuracy
- A good chart should not be deceptive, distorted, misleading, or in any

way susceptible to wrong interpretations as a result of inaccurate or
careless construction. Also, care should be taken so as not to create
any optical illusion.
An effective chart can be easily read and understood.
The graph

should focus on the message it is trying
to communicate.
There

should be an unambiguous representation of the facts.
The graph

must be able to aid the reader in the interpretation of facts.
The basic design of a statistical chart should be simple, straight-
forward, not loaded with irrelevant, superfluous, or trivial symbols
and ornamentation.
There should be no distracting elements in a

chart that inhibit effective visual communication.
A good chart is one that is designed and constructed to attract and
hold attention
by holding a neat, dignified,
and professional

appearance.
It must be artistic in that it embodies harmonious

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1. Line Chart - graphical presentation of data especially useful for showing trends over a

Market Shares of Leading Softdrinks in Metro Manila:

0
1989        1990        1991       1992       
1993

2. Pie Chart - a circular graph that is useful in showing how a total quantity is

distributed among a group of  categories.  The “pieces
proportions of the total that fall into each category.

Pe ps i                                     Coca-Cola
30%                                             40%

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2000
1999
1998
1997
1996
1995
1980
1975
1970•
- .10

3. Bar Chart - consists of a series of rectangular bars where the length of the bar

represents the quantity or frequency for each category if the bars are arranged
horizontally.
quantity.

If the bars are arranged vertically, the height of the bar represents the

4. Pictorial unit chart – a pictorial chart in which each symbol represents a definite and

Growth Pattern of Philippine Population: 1960 - 2000

0                     10                   20                  30                  40

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Definition.  The raw data is the set of data in its original form.

Example: Final grades of Soc Sci 101 Students

Definition.
An array is an arrangement of observations according to their magnitude, either in
increasing or decreasing order.

Example: Final grades of Soc Sci 101 Students arranged in an array

easier to detect the smallest and largest value
easier to find the measures of position

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In the construction of a frequency distribution, the various items of a series are classified into
groups.  The frequency distribution table shows the number of items falling into each group.

Class frequency
Class interval
Class limits
Class boundaries

the number of observations falling in the class
the numbers defining the class 
the end numbers of the class
the true class limits; the lower class boundary (LCB) is usually
defined as halfway between the lower class limit of the class and the
upper class limit of the preceding class while the upper class
boundary (UCB) is usually defined as halfway between the upper
class limit of the class and the lower class limit of the next class
the difference between the upper class boundaries of the class and the
preceding class; can also be computed as the difference between the
lower class boundaries of the current class and the next class; can also
be computed by using the respective class limits instead of the class
boundaries
midpoint of a class interval
a class that has no lower limit or upper limit

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