3rd Quarter - Statistics and Probability

Statistics

● Latin word “status” which means state

● A science (branch of Mathematics) that deals

with collection, presentation, analysis, and
interpretation of data.
Population vs. Sample
Branches of Statistics
POPULATION
1. Descriptive Statistics
● Is defined as group of people, animals, places,
2. Inferential Statistics things or ideas to which any conclusion based on
characteristics of sample will be applied.
Descriptive Statistics
● Totality
● summarizes or describes the important
characteristics of a given set of data. SAMPLE

● It involves the collection, organization, ● a subset or sub-collection or portion of elements

summarization, and presentation of data. It is drawn from a population.
being applied once the set of data refers to a
population or to a sample. Parameter vs. Statistic

● Parameter – describes the population, refers to

specific characteristic of the population subject
of interest or subject of investigation that is
measurable.

● Statistic – describe the samples, refers to the

characteristics of the samples

How to know if it is Statistic or Parameter?

● Focus on which respondents is/are involve.

Inferential Statistics

● Aims to give information about the population

by studying the characteristics of the sample
drawn from it.

● It is the branch of statistics that interprets and

draws conclusions from data. It uses hypothesis
testing.
 ● Secondary Data – refer to information which is
taken from a secondary source.

STATISTICAL DATA

DATA Independent Data

● A result of experimentation, observation, ● Refer to any controlling data.
investigation and other means and often appears
as a numerical figure and then evaluated to make ● Data which are not affected by any other data.
it into useful knowledge.
Dependent Data
● Refers to any information concerning to a
● Any data that is affected by controlling data.
population or sample

Classification (Nature) of Data

1. Types of data according to SOURCE

2. Types of data according to FUNCTIONAL

RELATIONSHIP

3. Types or CATEGORIES of data

4. Classification of data according to SCALE OF

MEASUREMENT
Types or CATEGORIES of data
Types of data according to SOURCE
● Qualitative Data – uses
● Primary Data – refer to information which is categories or attributes that
gathered directly from the original source. are distinguished by some
non-numeric characterstics
 ● Quantitative Data – consist
of numbers representing
counts or measurements

● Types of Quantitative Data

● Discrete –
Countable

● Continuous –
Measurable

If the data is QUANTITATIVE

Interval – show likeness, differences and give

meaningful amounts between data. It does not have a
“true zero” starting point, instead it is arbitrarily
assigned

Ratio – modified interval level to include zero as a

starting point

Classification of data according to SCALES OF

MEASUREMENT

If the data is QUALITATIVE

Nominal – data that consists of names, labels, or

categories only 5 Steps in Statistical Investigation

Ordinal – measurements deal with order or rank, 1. Identification of the problem – formulate a problem
provides comparison but the degrees of difference are or concept that is worth to study, to be investigated, to
not available understand it

2. Collection of Data – refers to the different methods

and techniques of gathering the data.

3. Presentation of Data – refers to the tabulation and

organization of data in tables, graphs & chart.
4. Analysis of Data – the procesess of deriving relevant 2. Tabular Form - data are presented in tables (rows
information from the gathered data through the different and columns).
statistical tools.
- Row and column must be well
5. Interpretation of Data – refers to the task of drawing defined or labeled
conclusions or inferences from the analyzed data.
Parts of the table: Title, Row’s name, Column’s
name, cell description

3. Graphical Form - Data are presented in visual

forms.

Common Graphical Presentations:

Methods of Collecting Data
a. Bar Chart
DIRECT OR INTERVIEW METHOD
b. Pie Chart
 It is a method where there is a person to person
interaction. An exchange of idea between the c. Pareto Chart
soliciting information(interviewer) and the one
that is supplying the information (interviewee). d. Pictograph
This method is applicable in a small sample or e. Line Chart
population size.
f. Map Graph or Map Chart
INDIRECT OR QUESTIONNAIRE METHOD
Probability and Random Variable
 A questionnaire is a list of well-planned
questions written on paper which can be either Probability
personally administered or mailed by the
researcher to the respondents. ● Describes the level of certainty; (likelihood,
chance or possibility)
OBSERVATION METHOD
● Probability (outcome) can be expressed in
 A scientific method or gathering data that makes decimal, fraction or percentage
possible use of all senses to measure or to obtain
results from the subject of the study. ● Probability Distribution – is a table, graph,
formula or notation which supplies the
REGISTRATION METHOD probability of a given outcome’s occurrence.

 A documentary analysis wherein data are Random Variables

gathered from fact or information on file.
Examples are births, death, license, land lines, ● A variable determined by chance, denoted by x.
company registration etc.
● A numerical description of the outcome of a
EXPERIMENT METHOD statistical experiment

 A method of collection of data wherein effort is Solving Probability

made to control the factors affecting the variable
● Sample Space (n(S)) – set of all possible
in the question. It examines the Cause and Effect
outcomes of an experiment
of a certain phenomenon.
● Event (P(E)) – a subset of the sample space
Methods of Presenting Data
– set of all expected outcomes from the
1. Textual Form - data is presented in paragraph form
sample space
 ● Experiment – simple process of noting an ○ Ex: at most 3 tails -> sum of 3 tails and
outcome below

● Outcome – a direct measurement or answer

obtained after an experiment

Formula:

expected outcome
Probability of an Event = “and” vs. “or” vs. “not”
total outcome

n(e) AND – getting the common between the 2 conditions

● P(E)=
n(s) Ex. Getting king and black card
Example – Total number of outcomes -> you will get the common between king and
black card

OR – getting the values of all 2 conditions

*take note: you will count as one the values that have
common

Ex. Getting king or black card

-> you will get the all king and black card

NOT – not including in the values the given condition

Ex. Not getting a king card

-> you will get all card except the king card.

“At least” vs “At most”

● At least – getting all the sum of probabilities

starting from the given to highest condition.
Sum of Dice
○ Ex: at least 2 tails -> sum of 2 tails and
above

● At most – getting all the sum of probabilities

starting from the given to lowest condition.
Number in Dice Tables of Areas under the Normal Curve

• Also known as z – Table

• The z – score is a measure of relative standing.

• It is calculated by subtracting μ from the

measurement X and the dividing the result by σ

• The final result, the z – score, represents the

distance between a given measurement X and
the mean, expressed in standard deviations.
Either the z – score locates X within sample or
within a population.

Normal Curve

● Gaussian distribution

● A bell-shaped frequency distribution curve.

● Most of the data values in a normal distribution

tend to cluster around the mean. Exploring the z – scores
● A normal curve has 3 divisions: The areas under the normal curve are given in terms of z
– values or scores. Either the z – scores locates X within
● predictable SDs that follow the
a sample or within a population.
● 68%, 95%, 99.7% rule.
The formula for calculating z is:
● The total area is 100%
 X−μ
z= (z – score for population data)
σ

X− X
z= (z – score for sample data)
s

Where:

X = given measurement

μ = population mean

σ = population standard deviation

X = sample mean

s = sample standard deviation

Exploring the z – scores: Conditions

You need to look out for the words similar to it to

identify what conditions to apply.