1.1 Stats and types of statistics

applied statistic
- Descriptive statistics: summarizing data through measures such as mean, median, and standard deviation.
- Inferential statistics: making predictions or generalizations about a population based on a sample.

Inferential stats

an element or member of a sample or population is a specific subject or object
A variable is a characteristic under study that assumes
different values for different elements. In contrast to a
variable, the value of a constant is fixed
the value of a variable for an element is called an observation or measurement
A data set is a collection of observations on one or more
variables

quantitative variables (can be measured numerically)
- discrete variables
- continuous variables
qualitative or categorical variables (cannot be a numerical value but can be classified into two or more nonnumeric categories)
a variable that can assume any number between intervals is a continuous variable, whereas discrete variables take on a finite number of values, often represented as counts or whole numbers.

Examples

Theoretical stats
applied statistic
- Descriptive statistics: summarizing data through measures such as mean, median, and standard deviation.
- Inferential statistics: making predictions or generalizations about a population based on a sample.

Inferential stats

an element or member of a sample or population is a specific subject or object
A variable is a characteristic under study that assumes
different values for different elements. In contrast to a
variable, the value of a constant is fixed
the value of a variable for an element is called an observation or measurement
A data set is a collection of observations on one or more
variables

quantitative variables (can be measured numerically)
- discrete variables
  - Examples: number of children in a household, number of cars owned, number of defects in a product.
- continuous variables
  - Examples: height of a person in cm ( $h = 175.5$ ), weight of an object in kg ( $w = 65.2$ ), temperature in Celsius ( $T = 25.7^ ext{o}C$ ), time taken to complete a task in minutes ( $t=12.3$ ).
qualitative or categorical variables (cannot be a numerical value but can be classified into two or more nonnumeric categories)
- Examples: hair color (e.g., black, brown, blonde), gender (e.g., male, female), marital status (e.g., single, married, divorced), brand of a product (e.g., Apple, Samsung).
a variable that can assume any number between intervals is a continuous variable, whereas discrete variables take on a finite number of values, often represented as counts or whole numbers.

Data collected on diff elements at the same point in time or for the same period of time is call cross-section data
Data collected on the same element for the same variable at
different points in time or for different periods of time are
called time-series data

population refers to all individuals who are being studied. the population is also called the target population
a portion of the population selected is a sample, which is used to make inferences about the entire population without needing to collect data from all individuals.
A survey that includes everyone is called a census
- sample survey is a portion of people
a sample that represents the characteristics of the population as a whole is called a representative sample
random vs. non-random sample
- random sample means everyone has a chance of being selected
- non-random means some people are excluded from being selected
sampling error vs. non-sampling error
- the sampling error is the diff between the result of a sample survey and if the whole population was included