Probability and statistics (basic statistical concepts)
Probability and Statistics
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
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
Basic Statistical Concepts
1. A bowler wants to find his
bowling average for the past 12
1. A bowler wants to estimate his
chance of winning a game based on
his current season averages of his
2. A Housewife wants to determine
the average weekly amount she
spent on groceries in the past 3
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
Samples selected randomly from populations
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
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
The sufficiency of sample size in surveys can be
obtained by using the Slovin’s formula:
n = N
1 + N e2
n= is the sample size
N= is the population
e= estimated level of error
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?
Parameter – is a numerical characteristic of the
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
A variable is a characteristic that changes or varies over
time and/or for different individuals or objects under
Qualitative Variables – measure a quality or characteristic on
each individual or object. It is a variable that yields categorical
(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)
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
First level of measurement is called the nominal level.
Example: classifying objects by gender, marital status
Second level of measurement is called the ordinal
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.
A. In each of these statements, tell whether
descriptive or inferential statistics have been
1. 6 out of 45 computers in the computer laboratory
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.
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.