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 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

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

Graphical form

Samples selected randomly from populations

Paired Measures

Statistical Techniques

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 situation.

Example

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 sizeN= is the populatione= estimated level of error

Slovin’s Formula

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

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

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

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 level.

Data measured can be ordered or rankedExamples: 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

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

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.

Percentages

Summation

Properties of Summation

Examples