🔸Statistics is a branch of mathematics that deals with collecting, organizing, and interpreting data to address a certain phenomenon.

Example: Marketing strategists use statistics to see the current market trend and devise solutions on how companies could sell more of their products.

🔸Population is the set of all possible cases from which data are collected.

Example: A study regarding the average height of students in a school requires the set of all students studying in that school as its population.

🔸Sample is a subset of the population under study.

Example: A study regarding the average height of students in a school may focus only on the sample set of students in a single grade level studying in that school.

🔸Variables are characteristics that vary over time from subject to subject.

Example: Consider a study regarding the influence of social media on students' preferences in choosing a student leader. In this study, a researcher may  include the number of social media accounts per sample student as one of the  variables. The researcher can also choose the gender of the sample student as another variable.

🔸Qualitative Variable is a type of variable that focuses on the quality or characteristics of each experimental unit.

Example: Civil Status, Gender, Color, Favorite Movie

🔸Quantitative Variable is a type of variable that measures a numerical quantity on each experimental unit.

Example: Age, Height, Weight, Daily Allowance

🔸Data Collection is the process of gathering data such as surveys, interviews, etc.

🔸Sampling is the process of selecting subset of the population.

METHODS OF DATA COLLECTION

a. Surveys and Questionnaires: 

Description: Surveys involve asking individuals a set of predetermined questions, often in written form, to gather information about their opinions, behaviors, or characteristics.

Application: Used in social sciences, market research, and public opinion polls

Advantages: Cost-effective, can reach a large audience, standardized format

Challenges: Response bias, limited depth of information

b. Interviews:

Description: Interviews involve direct interaction between a researcher and a participant, where questions are asked and responses are recorded.

Application: Common in qualitative research, case studies, and in-depth investigations

Advantages: Allows for in-depth exploration, flexibility in questioning, and clarification of responses

Challenges: Time-consuming, potential for interviewer bias

c. Observations:

Description: Researchers directly observe and record behavior, events, or phenomena without direct interaction with the participants.

Application: Used in naturalistic studies, ethnography, and behavioral research

Advantages: Provides firsthand information and minimizes response bias

Challenges: Observer bias, limited insight into underlying motivations

d. Experiments:

Description: Researchers manipulate variables to observe the effect on the outcome. Controlled conditions help establish cause-and-effect relationships.

Application: Common in natural sciences, psychology, and medicine

Advantages: Allows for causal inference, high internal validity

Challenges: Artificial settings may limit generalizability, ethical concerns

e. Case Studies:

Description: In-depth examination of a single case or a small number of cases to gain insights into complex phenomena.

Application: Common in psychology, medicine, and social sciences

Advantages: Rich, detailed information, suitable for complex or unique cases

Challenges: Limited generalizability, potential for researcher bias

SAMPLING TECHNIQUES

a. Simple Random Sampling: Every individual in the population has an equal chance of being selected.

b. Stratified Sampling: Dividing the population into subgroups (strata) and then randomly sampling from each subgroup.

c. Systematic Sampling: Selecting every nth individual from the population after a random start.

🔸A statistical table is used to organize data and to display it graphically.

🔸The frequency distribution table is a statistical table that deals with the frequency or number of occurrences of a given variable for a specific experimental unit.

🔸Statistical Graphs or Charts are visual representations of statistical data. These graphs are utilized to illustrate a data set, making it simpler to understand and interpret the information.

🔸A pie graph is a circular graph that shows how the categories are distributed. It shows the division of a whole into its parts. It is used to convey information on different categories, like business, sciences, and education.

🔸Bar Graph is a data presentation tool that uses bars with different heights and lengths. To create a bar graph, plot the frequencies against the categories.

🔸The line graph makes use of lines and dots to show a potential future pattern or trend. A line graph works well for presenting time series. 

🔸Stem and Leaf Plot is a unique table in which each data value is divided into a "stem" (the first digit or digits) and a "leaf" (typically the last digit).

🔸Integers are numbers that include the natural numbers, their opposites (the negative integers), and zero. An integer is greater than another integer if the first integer is to the right of the second integer on the number line. An integer is less than another integer if the first integer is to the left of the second integer on the number line. 

Integers are numbers that include the natural numbers, their opposites (the negative integers), and zero.

🔸GEMDAS stands for Grouping, Exponents, Multiplication and Division, and Addition and Subtraction. This means that in simplifying numerical expressions, the operation one should work on first is the Grouping symbols (parenthesis, brackets, or braces), then Exponents, Multiplication and Division next, and lastly Addition and Subtraction. That is, in simplifying numerical expressions, the order of operations should follow GEMDAS.

🔸The absolute value of an integer refers to its actual distance from zero in a number line. It is denoted by the  symbol  |𝑥| , where 𝑥 is any positive or negative integer, or zero