The document discusses key concepts in probability and statistics. It defines statistical and descriptive methods, and explains that descriptive methods are used to collect and analyze data from a sample, while inferential methods make predictions or decisions with uncertainty. Basic statistical concepts are also introduced, such as populations, samples, parameters, statistics, variables, and measurement scales. Descriptive statistics are used to summarize or describe characteristics of data, while inferential statistics are used to make predictions beyond the immediate data. Examples are provided to illustrate these fundamental probability and statistics terms and concepts.

1. Probability and Statistics

2.  Statistical Methods – are the mathematic techniques used
to facilitate the interpretation of numerical data secured
from entities, individuals or observations.
 Statistic – used to denote a particular measure or formula
such as an average, an index number or a coefficient of
correlation.
 Descriptive – methods concerned with the collection,
description, and analysis of a set of data using only the
information gathered from a subset of this larger set.
 Inferential – make use of generalizations, predictions,
estimations, or more generally decisions in the face of
uncertainty.
Basic Statistical Concepts

3. Descriptive Inferential
1. A bowler wants to find his
bowling average for the past 12
games.
1. A bowler wants to estimate his
chance of winning a game based on
his current season averages of his
opponents.
2. A Housewife wants to determine
the average weekly amount she
spent on groceries in the past 3
months.
2. 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.
Descriptive vs Inferential

4.  Graphical form
 Samples selected randomly from populations
 Paired Measures
Statistical Techniques

5.  A Population is a collection of all the elements under
consideration in a statistical study and usually
denoted by a N.
 A Sample is a part or subset of the population from
which the information is collected and is usually
denoted by a n.
Population and Sample

6. 1. We may wish to draw conclusions bout the income
rate of 1000 manufacturing companies by examining
only 200 companies from this population.
2. A manufacturer of kerosene heaters wants to
determine if customers are satisfied with the
performance of their heaters. Toward this goal,
5000 of his 200,000 customers are contacted.
Identify the population and the sample for this
situation.
Example

7. The sufficiency of sample size in surveys can be
obtained by using the Slovin’s formula:
n = N
1 + N e2
where:
n= is the sample size
N= is the population
e= estimated level of error
Slovin’s Formula

8. 1.) A researcher is conducting an investigation regarding
the factors affecting the efficiency of the 185 faculty
members of a certain college. If he wanted to have a
margin of error of 5%, then how many of the faculty
members should be taken as respondents?
Example

9. Parameter – is a numerical characteristic of the
population.
Statistics – 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 0.08.
Identify the parameter and the statistics.
Parameter and Statistics

10.  A variable is a characteristic that changes or varies over
time and/or for different individuals or objects under
consideration.
 Qualitative Variables – measure a quality or characteristic on
each individual or object. It is a variable that yields categorical
responses.
(Example: Color of cars, t-shirt size, political affiliation,
occupation, marital status)
 Quantitative Variable – measure a numerical quantity or
amount on each individual or object, often represented by x.
(Example: Let x represent the number of female students
in a university, weight, height, no. of cars)
Variables

11.  Under Quantitative variables:
 A discrete variable can assume only a finite or countable
number of values.
(Example: Let x represent the number of graduates
produced by a school in a particular school year)
 A continuous variable can assume infinitely many values
corresponding to the point on a line interval.
(Example: Let x represent the daily tonnage produced by a
coal mining company)
Discrete and Continuous Variables

12.  First level of measurement is called the nominal level.
Example: classifying objects by gender, marital status
 Second level of measurement is called the ordinal
level.
Data measured can be ordered or ranked
Examples: teacher ratings, year level
 Third level of measurement is called the interval level.
Has precise differences between measures but there
is no true zero.
Examples: IQ level, temperature(in Celsius)
 Final level of measurement is called the ratio level.
Examples of ratio scale are those used to measure
height, weight, or area.
Measurement Scales

13. A. In each of these statements, tell whether
descriptive or inferential statistics have been
used.
1. 6 out of 45 computers in the computer laboratory
are defective.
2. This year, the net income of LEN Company
increased by 20%.
3. In 2010, the sales volume of ABC Company will
increase by 15%
4. Seven out of ten on-the-job injuries are men.
5. The average number of absences of employees in
a company was 14 per year.
Exercise

14. B. Classify each as nominal level, ordinal level, interval
level, or ratio-level measurement.
1. Pages in your Calculus textbook.
2. Temperatures at Tagaytay.
3. Rankings of basketball teams in the NBA.
4. Times required for a student to finish a quiz.
5. Salaries of the top CEO of SM.
6. Marital status of teachers at Don Bosco.

15. Percentages

16. Summation

17. Properties of Summation

18. Examples