Unlocking the Power of Statistics

Unlocking the Power of Statistics

Discover the potential of statistics in unlocking insights, making informed decisions, and driving success in various fields. Explore the key concepts, techniques, and applications that can empower you to harness the power of data.

Unlocking the Power of Statistics

Statistics is divided into two main branches: Descriptive and Inferential. Descriptive statistics involves summarizing and presenting data, while inferential statistics involves making inferences and drawing conclusions from data. Understanding the population and sample, as well as sample size determination using formulas like Cochran and Yamane, is crucial. Sampling techniques, such as random and non-random sampling, are used to select representative samples. Statistical data includes description, source, and level of measurement. Statistics plays a vital role in modern world mathematics and data management.

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS
Definition
Divisions of Statistics

Descriptive
Inferential

Population and Sample
Sample Size

Cochran
Yamane

Sampling Techniques

Random Sampling
Non Random

Statistical Data

Description
Source
Level of
Measurement

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS
Definition
Divisions of Statistics

Descriptive
Inferential

Population and Sample
Sample Size

Cochran
Yamane

Sampling Techniques

Random Sampling
Non Random

Statistical Data

Description
Source
Level of
Measurement

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS
Definition
Divisions of Statistics

Descriptive
Inferential

Population and Sample
Sample Size

Cochran
Yamane

Sampling Techniques

Random Sampling
Non Random

Statistical Data

Description
Source
Level of
Measurement

Multiple Choice

In an interval scale, zero
indicates the absence of
the attribute being
measured.

• TRUE

• FALSE

Multiple Choice

Which scale of measurement has
a true zero point?

• NOMINAL

• ORDINAL

• INTERVAL

• RATIO

Multiple Choice

Qualitative data can be easily
quantified and used in
mathematical calculations.

• TRUE

• FALSE

Multiple Choice

Orders objects, but differences between objects are not
meaningful.

• NOMINAL

• ORDINAL

• INTERVAL

• RATIO

Multiple Choice

Allows for the meaningful calculation of differences and ratios.

• NOMINAL

• ORDINAL

• INTERVAL

• RATIO

Multiple Choice

Classifies and categorizes objects without any order.

• NOMINAL

• ORDINAL

• INTERVAL

• RATIO

Multiple Choice

Orders objects and allows for the calculation of meaningful
differences, but lacks a true zero point.

• NOMINAL

• ORDINAL

• INTERVAL

• RATIO

Multiple Choice

What is the primary disadvantage of using
secondary data in statistical analysis?

• It is more time-consuming to collect.

• It may not precisely fit the specific needs
  of the current study.

• It is less accurate than primary data.

• It always requires a larger sample size.

DATA MANAGEMENT

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS

Methods of Data
Gathering

Interview Method
Questionnaire
Registration
Observation
Experiments

METHODS OF DATA COLLECTION

A. Interview (Direct) Method – a method of person-to-person

exchange between the interviewer and the interviewee.

Positive:
1. It provides consistent and more precise information since

clarification maybe given by the interviewee.

2. Questions may be repeated or maybe modified to suit the

interviewee’s level of understanding.

Negative:
1. Time-consuming
2. Expensive
3. Limited field coverage

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS

Methods of Data
Gathering

Interview Method
Questionnaire
Registration
Observation
Experiments

METHODS OF DATA COLLECTION

B. Questionnaire (Indirect) Method – in this method written

responses

are

given

to

prepared

questions.

A

questionnaire is used to elicit answers to the problems of
the study. Questionnaires may be mailed or hand-carried.

Positive:
1. Inexpensive
2. Can cover a wide area in a shorter span of time.
3. Respondents may feel a greater sense of freedom to

express views and opinions because their anonymity is
maintained.

Negative:
1. There’s a strong possibility of non-response, especially

when questionnaires are mailed.

2. Questions not easily understood may not be answered.

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS

Methods of Data
Gathering

Interview Method
Questionnaire
Registration
Observation
Experiments

METHODS OF DATA COLLECTION

C. Registration

Method

–

this

method

of

gathering

information is enforced by law.

Example:

❏ registration of births
❏ deaths
❏ vehicles
❏ licenses

Positive:
1) Information is kept systematized.
2) Information is always made available to the public.

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS

Methods of Data
Gathering

Interview Method
Questionnaire
Registration
Observation
Experiments

METHODS OF DATA COLLECTION

D. Observation Method – the investigator observes the

behavior of the subject/respondent. It is used when the
subjects cannot talk or write.

Positive:
The recording of behavior at the appropriate time and
situation is made possible.

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS

Methods of Data
Gathering

Interview Method
Questionnaire
Registration
Observation
Experiments

METHODS OF DATA COLLECTION

E. Experiment Method - this method is used when the

objective is to determine the cause-and-effect relationship
of certain phenomena under controlled conditions.

It is

usually used by scientific researches.

Mathematics in the

Modern World

DATA MANAGEMENT

STATISTICS

Methods of Data
Gathering

Interview Method
Questionnaire
Registration
Observation
Experiments

Multiple Choice

What is the primary advantage of the
Interview Method in data gathering?

• It is less expensive.

• It provides more consistent and
  precise information.

• It covers a wider field.

• It is less time-consuming.

Multiple Choice

The Questionnaire Method
is more expensive than the
Interview Method.

• TRUE

• FALSE

Multiple Choice

What is the main purpose of the
Experiment Method in data gathering?

• To observe natural behaviors.

• To gather information enforced by law.

• To determine the cause-and-effect
  relationship under controlled conditions.

• To gather qualitative data.

Multiple Choice

Information is systematic and publicly
available.

• Interview

• Questionnaire

• Registration

• Experiment

Multiple Choice

It provides the opportunity for clarification.

• Interview

• Questionnaire

• Registration

• Experiment

Multiple Choice

Maintains respondent anonymity.

• Interview

• Questionnaire

• Registration

• Experiment

Multiple Choice

A good
question in a questionnaire
must be biased to obtain
specific responses.

• TRUE

• FALSE

Multiple Choice

What is a key feature of good
questions in a questionnaire?

• They should be complex.

• They should be leading.

• They should be clear and
  simple.

• They should be vague.

Data Presentation

Textual
Data is presented in a narrative form

Methods of Data Presentation

Detailed explanation
Best used with less data

Ineffective when data is
large

Textual
Data is presented in a narrative form

Detailed explanation
Best used with less data

Ineffective when data is
large

Tabular
Data is presented in rows and columns

Helps in comparing data
Organized

Not fully detailed

Tabular

Data is presented in rows and columns
2

Helps in comparing data
Organized
Not fully detailed

Statistical Table

Boxhead

Body

Stub

Table

Heading

Tabular

Data is presented in rows and columns
2

Helps in comparing data
Organized

Not fully detailed

Statistical Table

Table Heading

Tabular

Data is presented in rows and columns
2

Helps in comparing data
Organized

Not fully detailed

Statistical Table

Stub

Row

captions

Tabular

Data is presented in rows and columns
2

Helps in comparing data
Organized

Not fully detailed

Statistical Table

Boxhead

Column Captions

Stub Head

Tabular

Data is presented in rows and columns
2

Helps in comparing data
Organized

Not fully detailed

Statistical Table

Body

Tabular

Data is presented in rows and columns
2

Statistical Table

Boxhead

Body

Stub

Table

Heading

Graphical
Data is presented in visual form

Provides visual analysis
More comprehension

Costly
Problem of suitability

Bar Graph

Consists of bars of equal
widths
Used best for large changes
over time/category

Kinds of Graphs and Diagrams

Bar Graph

Consists of bars of equal
widths
Used best for large changes
over time/category

Line Graph

Shows relationships between
two or more sets of quantities
Used best for small changes
over time/category

Line Graph

Shows
relationships
between two or
more sets of
quantities
Used best for
small changes
over
time/category

Methods of
Data Presentation

Circle/Pie Graphs

Represents quantities that make
up a whole
Not used for data that changes
over time

Circle/Pie Graphs

Represents quantities that make
up a whole
Not used for data that changes
over time

3.4
Methods of Data Presentation

= 50

School
Students that
donated blood

Saint Louis University

University of Baguio

University of the

Cordillera

Pictogram

Symbols that
represent
values of the
data

Map graph/
Cartogram

Used best for
representing
geographical
data

Histogram

•Simply a bar chart of a frequency distribution.
•FREQUENCY DISTRIBUTION is a data grouped into

different classes or interval.

To construct a
histogram from a
continuous variable you
first need to split the
data into intervals
called bins.

Stem-and-Leaf Plots

•Numerical data are sorted according to a pattern

which involves separating each element in the data
set into two parts, called the stem and the leaf.

•Decide what units will be used for the stem and for

the leaves in a way that there will be 5 to 20 stems.

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Example:

Consider the following data to illustrate how to

construct a histogram and stem-and-leaf displays.

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Bin

Example:

Consider the following data to illustrate

how to construct a histogram and stem-
and-leaf displays.

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Bin

30.1 - 31.1

Example:

Consider the following data to illustrate

how to construct a histogram and stem-
and-leaf displays.

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Example:

Consider the following data to illustrate

how to construct a histogram and stem-
and-leaf displays.

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Bin

30.1 - 31.1

31.1 - 32.1

Example:

Consider the following data to illustrate

how to construct a histogram and stem-
and-leaf displays.

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Bin

30.1 - 31.1

31.1 - 32.1

32.1 - 33.1

Bin

Values

Frequency

30.1 - 31.1

31.1 - 32.1

32.1 - 33.1

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

31.1 - 32.1

32.1 - 33.1

32.0

32.3

32.6

31.7

31.4

32.7

31.4

32.5

31.2

31.8

31.9

32.8

31.5

31.6

32.2

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

6

31.1 - 32.1

32.1 - 33.1

32.0

32.3

32.6

31.7

31.4

32.7

31.4

32.5

31.2

31.8

31.9

32.8

31.5

31.6

32.2

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

6

31.1 - 32.1

32.1 - 33.1

32.0

32.3

32.6

31.7

31.4

32.7

31.4

32.5

31.2

31.8

31.9

32.8

31.5

31.6

32.2

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

6

31.1 - 32.1

31.2, 31.4, 31.4,
31.5, 31.6, 31.7,
31.8, 31.9, 32.0

32.1 - 33.1

32.3

32.6

32.7

32.5

32.8

32.2

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

6

31.1 - 32.1

31.2, 31.4, 31.4,
31.5, 31.6, 31.7,
31.8, 31.9, 32.0

9

32.1 - 33.1

32.3

32.6

32.7

32.5

32.8

32.2

32.3

32.6

32.7

32.5

32.8

32.2

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

6

31.1 - 32.1

31.2, 31.4, 31.4,
31.5, 31.6, 31.7,
31.8, 31.9, 32.0

9

32.1 - 33.1

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

6

31.1 - 32.1

31.2, 31.4, 31.4,
31.5, 31.6, 31.7,
31.8, 31.9, 32.0

9

32.1 - 33.1

32.2, 32.3, 32.5,
32.6, 32.7, 32.8

Illustration for Histogram:

Bin

Values

Frequency

30.1 - 31.1

30.1, 30.4, 30.6,
30.8, 30.8, 30.9

6

31.1 - 32.1

31.2, 31.4, 31.4,
31.5, 31.6, 31.7,
31.8, 31.9, 32.0

9

32.1 - 33.1

32.2, 32.3, 32.5,
32.6, 32.7, 32.8

6

Example:

Consider the following data to illustrate how to

construct a histogram and stem-and-leaf displays.

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

30.8

30.9

32.0

32.3

32.6

31.7

30.4

31.4

32.7

31.4

30.1

32.5

30.8

31.2

31.8

31.9

32.8

31.5

31.6

30.6

32.2

Stem

Leaf

Frequency

30
31

32

Illustration for Stem-and-Leaf Plot

32.0

32.3

32.6

31.7

31.4

32.7

31.4

32.5

31.2

31.8

31.9

32.8

31.5

31.6

32.2

Stem

Leaf

Frequency

30

1, 4, 6, 8, 8, 9

6

31

32

Illustration for Stem-and-Leaf Plot

32.0

32.3

32.6

31.7

31.4

32.7

31.4

32.5

31.2

31.8

31.9

32.8

31.5

31.6

32.2

Stem

Leaf

Frequency

30

1, 4, 6, 8, 8, 9

6

31

32

Illustration for Stem-and-Leaf Plot

32.0

32.3

32.6

32.7

32.5

32.8

32.2

Stem

Leaf

Frequency

30

1, 4, 6, 8, 8, 9

6

31

2, 4, 4, 5, 6, 7, 8, 9

8

32

Illustration for Stem-and-Leaf Plot

32.0

32.3

32.6

32.7

32.5

32.8

32.2

Stem

Leaf

Frequency

30

1, 4, 6, 8, 8, 9

6

31

2, 4, 4, 5, 6, 7, 8, 9

8

32

Illustration for Stem-and-Leaf Plot

Illustration for Stem-and-Leaf Plot

Stem

Leaf

Frequency

30

1, 4, 6, 8, 8, 9

6

31

2, 4, 4, 5, 6, 7, 8, 9

8

32

0, 2, 3, 5, 6, 7, 8

7

Total: 21

Multiple Choice

Which method of data presentation
emphasizes and compares important
figures through narrative?

• Textual Presentation

• Tabular Presentation

• Graphical Method

• Experiment Method

Fill-in-the-Blank:
A bar graph is best used
for showing large changes
over ______.

Multiple Choice

Represents quantitative data by separating each
value into two parts.

• Pie Chart

• Stemplot

• Ogive

• Histogram

Multiple Choice

Depicts qualitative data as slices of a circle.

• Pie Chart

• Stemplot

• Ogive

• Histogram

Multiple Choice

Uses class boundaries and cumulative frequencies.

• Pie Chart

• Stemplot

• Ogive

• Histogram

Multiple Choice

The Graphical Method of
data presentation is not
effective in attracting and
holding the reader’s interest.

• TRUE

• FALSE