Topic 1 ELEMENTARY STATISTICS.pptx

WHY TO STUDY STATISTICS?
• To evaluate printed numerical facts.
• To interpret the results of sampling or to perform
statistical analysis in your work
• To make inferences about the population using
information collected from the sample

What Do Statisticians Do?
• Gather data
• Summarize data
• Analyze data
• Draw conclusions and report the results of
their analysis

DEFINITION
 Is a group of methods
that are used to collect,
organize, present,
analyze and interpret
data to make decisions
(COPAI).
STATISTICS
 refers to numerical
facts.
Examples:
 Income of a family
 Number of
employees at the
company
 Number of enrolled
students in a class
 Starting salary of a
typical college
graduate

BASIC CONCEPTS
 Data
 are numbers or measurements that are collected as a result from observation,
interview, questionnaire experimentation, test and so forth.
 Element or members of a sample or population
a specific subject or object about which the information is collected.
 Variable
 is a characteristic under study that assumes different values for different elements.
 Observation or measurement
 is the value of a variable for an element

 Statistic
 a summary measure describing specific characteristic of the sample
e.g. sample mean, sample variance
 Parameter
 a summary measure describing specific characteristic of the population usually
denoted by Greek letters: μ (mu), σ (sigma), ρ (rho), λ (lambda), τ (tau), θ (theta), α
(alpha) and β (beta) e.g. population mean, population variance
 Population
 consists of all elements – individuals, items, or objects – whose characteristics are
being studied.
 Sample
 is a portion/part of a population selected for study.
BASIC TERMS

•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. Identify the
a) population, b) sample, c) parameter, and d) statistic.
a) Population: The set of students at a certain college.
b) Sample: The set of 200 students who were interviewed.
c) Parameter: The population proportion of students in a certain
college who smoke cigarettes.
d) Statistic: (0.12) the proportion of students in the sample who
smoke cigarettes.

STEPS IN STATISTICAL INQUIRY
1. Collection of data
 can be done through interview, questionnaires, tests observation, registration
and experiments
2. Organization of data
 categorizing and classifying data to make it more usable and understandable.
3. Presentation of data
 organization of data into tables, graphs, charts, or paragraphs.
4. Analyzation the data
 process of extracting from the given data relevant and noteworthy information
and this uses statistical tools or techniques.
5. Interpretation of data
 drawing of conclusions or inferences from the analyzed data.

TYPES/FIELD OF STATISTICS
1. DESCRIPTIVE STATISTICS
 Consists of methods for organizing, displaying, and describing data by using
tables, graphs, summary measures.
 Suppose we have information on the 2021 total sales of top 100 stores in Moises
Padilla.
• The whole set of numbers that represents the sales of the top 100 stores is
called a data set.
• The name of each store is called an element
• The sales of each store is called an observation.
 concerned with gathering, classification and presentation of data and the
collection of summarizing values to describe group characteristics of data.
Examples: Class average of examination, range of student scores, average salary,
means of managerial satisfaction, average return of investment.

2. INFERENTIAL STATISTICS
 consists of methods that use sample results to help make predictions.
deals with making decisions, inferences, predictions, or forecasts about
populations based on results obtained from a sample.
This is also called inductive reasoning or inductive statistics.
For example a company receive a shipment of parts from a manufacturer that are
to be used in CD players manufactured by this company. To check the quality of
the whole shipment, the company will select few items from the shipment, inspect
inspect them, and make a decision.
 Commonly-used inferential Statistical tools or techniques:
• Testing hypothesis using z-test, t-test, simple linear correlation, analysis of
Variance (ANOVA), chi-squares (x²), regression and time series analysis.

• Determine what type/field of Statistics:
1. A bowler wants to find his bowling average for the past 12 games.
2. A bowler wants to estimate his chance of winning a game based on his current
season averages and the averages of his opponent.
3. A housewife would like to predict based on last year's grocery bills, the
average weekly amount she will spend for this year.
4. A housewife wants to determine the average weekly amount she spent on
groceries in the past three months.
5. A politician wants to know the exact number of votes he received in the last
election.
6. A politician would like to estimate, based on an opinion poll, his chance of
winning in the upcoming election.

 POPULATION
 consists of all elements – individuals, items, or objects – whose characteristics are
being studied.
In statistics, a population does not necessarily mean a collection of people, it can, in
fact, be a collection of people or any kind of items such as books, television sets, or cars.
Some examples are: The percentage of all families who earn less than P120, 000.00 a
year for 2004; The 2004 gross sales of all companies in Manila.
 SAMPLE
is a portion/part of a population selected for study.
For example, the various election polls conducted in the recent 2022 presidential Election to
estimate the percentage of voters favoring various candidates in the presidential election is based
on only few hundred or a few thousand of voters selected from various precincts. In these case,
the population consist of all registered voters in the Philippines. The sample is made up of the few
hundred or a few thousand of voters who are included in an opinion wall.
POPULATION vs SAMPLE

Identify whether population or sample:
o Undergraduate students in CPSU
o 300 undergraduate students from different CPSU
Campuses
o All BEED students of CPSU Moises Padilla
o Selected BEED students from first year to fourth year.
POPULATION vs SAMPLE

 Raw data
 are in their original form and structure.
 Grouped data
 are placed in tabular form characterized by class intervals with
with corresponding frequency.
 Primary data
 are measured and gathered by the researcher that published
it.
 Secondary data
 are published by another researcher or agency.
TYPES OF DATA

1. QUANTITATIVE VARIABLES
 are variables that can be measured numerically
 yield numerical responses representing an amount or quantity.
Examples: height, weight, number of children, incomes, gross sales, stock process.
 Classifications of Quantitative Variables
a. Discrete Variables
• values are countable
• Can assume only certain values with no intermediate values.
• For examples, the number of cars sold on any day at a car dealer is a discrete variable because
the number of cars sold must be 0, 1, 2, 3. The number of cars sold cannot be between 0 and
1 or between 1 and 2. A few other examples are the number of people visiting a bank on any
days, the number of cars in a parking lot, the number of cattle owned by a farmer and the
number of employee in a company.
TYPES OF VARIABLES

b. Continuous Variables
 can assume any numerical value over a certain interval or
intervals.
 cannot take on finite values but the values are related/associated
with points on an interval of the real line.
 Examples: Height, weight, temperature
Another Example of this is the time taken to serve a customer by a
bank teller because it can assume any value, lets’ say between 5
seconds and 20 minutes.
TYPES OF VARIABLES

2. QUALITATIVE OR CATEGORICAL VARIABLES
 cannot assume numerical value but can be classified into two
or more nonnumeric categories.
 refers to the attributes or characteristics of the samples.
 Examples: Civil status, Religious Affiliation, brand of soap
TYPES OF VARIABLES
Beed
2c

1. NOMINAL SCALE
 applies to data that are divided into different categories and these are used only for
identification purposes only.
 The names given to different maker of cars, such as Toyota, Honda, Kia Pride, and
BMW are for identification purposes only.
 Other examples are: names of companies, gender of people, marital status.
2. ORDINAL SCALE
 applies to data that are divided into different categories that can be ranked.
 For example, suppose in a survey people are asked to evaluate a product as excellent,
excellent, good or poor. These categories that they can be ranked. We know that
excellent has the highest rank and poor has the lowest rank.
Other examples: class standing, employees position.
SCALES OF MEASUREMENT

3. INTERVAL SCALE
 applies to data that can be ranked and for which the difference between
two values can be calculated and interpreted.
 possesses the properties of the nominal and ordinal levels. The distances
between any two numbers on the scale are known and it does not have a
stable starting point (absolute zero).
 Consider the IQ scores of four students 90, 150, 85 and 145. Here we can
say that the difference between 90 and 150 is the same as the difference
between 85 and 145 but we cannot claim that the second student is twice
as intelligent as the first.
Temperature possesses an interval scale of data, test result
 you can measure height in zero but you can also measure it in negatives.

4. RATIO SCALE
 applies to data that can be ranked and for which all arithmetic operation
(addition, subtraction, multiplication, and division) can be done.
 possesses all the properties of the nominal, ordinal and interval scales.
 Has an absolute zero point. (zero possesses a meaningful value)
 No negative value
 Common examples: duration, mass...
 years of teaching experience, years of military experience, Daily
Allowance, Weight (in kg)

SAMPLING
 is a process used in statistical analysis in which a
predetermined number of observations are taken from a
whole/larger population.
SAMPLING TECHNIQUE

1. PROBABILITY SAMPLING
 a sampling procedure where every element of a population is given a chance of
being selected as a number of a sample.
A. Random Sampling
 done by lottery or with the aid of a Table of Random Numbers, or the random
function of calculator.
 A restaurant leaves a fishbowl on the counter for diners to drop their business
cards. Once a month, a business card is pulled out to award one lucky diner with
a free meal. Another example: At a bingo game, balls with every possible number
are placed inside a mechanical cage. The caller rotates the cage, tumbling around
the balls inside. Then, she selects one of the balls at a random to be called, like B-
12 or O-62.
TYPES OF SAMPLING TECHNIQUE
Beed
2a

B. Systematic Sampling
 an alternative to simple random sampling especially when the population is
too big that random sampling becomes tedious. Random starting point is
selected from the list of population. The samples are determined by choosing
every nth element on the list until the desired number of samples are drawn.
 A researcher wanted to select a random group of 1, 000 people from a
population of 50, 000 using systematic sampling, all the potential participants
must be placed in a list and a starting point would be selected. Once the list is
formed, every 50th person on the list (starting the count at the selected
starting point) would be chosen as a participant, since 50, 000/1000=50.

C. Stratified Random Sampling
 done by creating different classes or strata within the population. The
grouping may be done based on grade level, income groupings, and gender,
among others.
 You need a sample size of 6. Two members from each group (yellow, red,
and blue) are selected randomly. Make sure to sample proportionally: in this
simple example,
1
3
of each group (
2
6
yellow,
2
6
red,
2
6
blue) has been sampled. If
you have one group that’s different size, make sure to adjust your proportions.
For example, if you had 9 yellow, 3 red, and 3 blue, a 5- item sample would
consist of
3
9
yellow (i.e. one third),
1
3
red,
1
3
blue.

D. Cluster Sampling
 if the population is too big, a sampling method maybe employed to a
smaller area. The population may be divided geographically into regions,
divisions, or districts.
• Suppose a researcher wants to survey academic performance of High School
students in Spain;
 He can divide the entire population into different clusters (cities).
 Then the researcher selects a number of clusters depending on his
research through simple or systematic random sampling.

In Stratified random sampling, all the strata of the population
is sampled while in cluster sampling, the researcher only randomly
selects a number of clusters from the collections of clusters of the
entire population. Therefore, only a number of clusters are sampled,
all the other clusters are left unpresented.
2. Non-Probability Sampling
 this is a sampling procedure in which not every element of the
population is given an equal chance of being selected as a
sample. The drawing of samples is based purely on the
researcher’s objectives.
TYPES OF SAMPLING
TECHNIQUE

A. Convenience Sampling
 the researcher’s convenience is the primary concern in using this method. For
instance, is the convenience of having internet connections will be considered, not
every element of a population is given a chance to be chosen as a sample since not
everyone has access to this technology.
• Using subjects that are selected from a clinic, a class or an institution that is easily
accessible to the researcher. A more concrete example is choosing five people from a
class or choosing the first five names in the list of patients.
• For instance, if you’re a marketing student who has been given task to get
feedback on “scope of content marketing in 2018”, you’d quickly create an online
survey and send a link to all the contacts on your phone, share a link on social media
and also talk to people you meet daily face-to-face.

B. Quota Sampling
 similar to stratified sampling but the drawing of samples in quota sampling
is not done randomly. If the desired quota is reached, the drawing of samples
is terminated.
 Let’s say you are performing a promotions related study to include 600
people, and you are required to include 300 women. Your quota(300 women)
would prevent you from using a typical random selection method, like simple
random sampling, because you’ll probably end up with something other than
300 women. Therefore your selection method won’t be probabilistic, and
you’ll be performing quota sampling.

C. Purposive Sampling/Judgmental Sampling
 used when the specific objective under study requires a particular sample
which may not cover the entire population.
 Consider a scenario where a panel decodes to understand what are the
factors which lead a person to select ethical hacking as a profession. Ethical
hacking is a skill which has been recently attracting youth. More and more
people are selecting it as a profession. The researchers who understand what
ethical hacking is will be able to decide who should form the sample to learn
about it as a profession. That is when judgmental sampling is implemented.
Researchers can easily filter out those participants who can be eligible to be a
part of the research sample.

Topic 1 ELEMENTARY STATISTICS.pptx

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