Introduction to Statistics: Concepts, Methods, and Applications, Summaries of Mathematics

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STATISTICS

• is the branch of mathematics which deals with the collection, organization and interpretation of data.

Note: STATISTIC

refers to a

numerical datum.

WHAT IS STATISTICS?

STATISTICAL METHODS OF APPLIED STATISTICS

• It refers to procedures and technique in the collection, presentation, analysis and interpretation of data.

FIELDS OF STATISTICS

STATISTICAL THEORY OF MATHEMATICAL STATISTICS

• It deals with the development and exposition of theories that serve as bases of statistical methods.

FIELDS OF STATISTICS

DESCRIPTIVE STATISTICS

• A bowler wants to find his bowling average for the past 12 games.

DESCRIPTIVE VS. INFERENTIAL

INFERENTIAL STATISTICS

• A bowler wants to estimate his chance of winning a game based on his current season averages and the averages of his opponents.

DESCRIPTIVE STATISTICS

• Collect Data e.g. Survey
• Present Data e.g. Tables and Graphs
• Characterize Data e.g. Mean

DESCRIPTIVE VS. INFERENTIAL

DESCRIPTIVE VS. INFERENTIAL

Examples:

1. A newspaper article reports the average salaries of health practitioners based on the average salaries obtained from samples in different health centers and hospitals.
2. A social psychologist is interested in determining whether individuals who graduate from technical vocational schools earn more than those who finished a four-degree college degree. He gathered data relative to the study and presented the results using tables and graphs.
3. A study of 250 patients admitted to a hospital during the past year revealed that, on the average, the patients lived 15 miles from the hospital. This was used to determine the average distance of residences of patients in the population.

DESCRIPTIVE VS. INFERENTIAL

Examples:

1. A correlational study is conducted on a sample-the finding was used to determine the relationship between family income and nutritional status of the children in the population.
2. A study aimed to determine the frequency of participation and extent of competence of BSE students in Statistics. Results obtained from a sample of students showed that they are moderately competent.
3. A study is conducted on a sample to determine the significant differences in the extent of utilization of the worldwide web between the freshmen and the seniors in a certain university. The perceptions of 200 freshmen and 150 seniors were obtained and presented and compared using tables and graphs

POPULATION and SAMPLE

Example: Audrey is interested about mobile phones used by the employees in her company. Population: collection of all values/prices of cellular phones owned by the employees in the company. Sample: any part of population, say, the values of the cellular phones owned by randomly selected employees 910 from each department) Example: Dina Maala wants to study the satisfaction of customers on her restaurant service. Population: all customers in the restaurant Sample: customers between 10 am to 2 pm

VARIABLES

• It is a characteristics or attribute of persons or objects which can be assume different values or labels for different person or objects under consideration.

Data

• it is any set of observation.

CATEGORICAL (Qualitative)

• are data which can be classified into groups or categories. Examples:
  1. Attitudes of workers in a company towards their superiors.
  2. Problems encountered of students in accomplishing modules

NUMERICAL (Quantitative)

• values of variables expressed in

numerical terms.

Examples:

1 .Number of rooms and hospital

admissions.

2. Monthly income of families in

your barangay.

NUMERICAL (Quantitative)

3. Level of competence of Math

students

4. Age of pregnant women

5. Degree of seriousness of

problems encountered