Probability and statistics (basic statistical concepts)Presentation Transcript
Probability and Statistics
Basic Statistical Concepts
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.
Descriptive vs Inferential
Samples selected randomly from populations
Population and Sample
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.
Example 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.
Slovin’s Formula 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
Example 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 and Statistics 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.
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)
Discrete and Continuous Variables
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)
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.
Exercise In each of these statements, tell whether descriptive or inferential statistics have been used. 6 out of 45 computers in the computer laboratory are defective. This year, the net income of LEN Company increased by 20%. In 2010, the sales volume of ABC Company will increase by 15% Seven out of ten on-the-job injuries are men. 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.