mgp87 / Statistics_for_DataScience

Statistics_for_DataScience

What are data?

Data Types

Category	Type	Description	Example
Numerical (numbers)	Interval	Numeric scale with meaningful intervals	Temperature in Celsius
Numerical (numbers)	Ratio	Numeric scale with a true zero point	Height
Numerical (numbers)	Discrete	Countable number of values	Number of students
Categorical (labeled)	Ordinal	Categories with a natural order, discrete, no necessarily meaningful intervals	Letter grades
Categorical (labeled)	Nominal	Categories without a natural order, discrete	Music genres

Examples:

• Discrete: Number of items purchased in January
• Ordinal: Favorite cities
• Nominal: Last five cities visited
• Ratio: Land area of a country
• Interval: Temperature in Celsius

Sample vs Population

• Population: The entire group we are interested in
• Sample: A subset of the population (ideally representative and randomly selected)

Examples:

• Population: All students in a school, number of snakes in the zoo
• Sample: Average of student grades in a classroom, opinion of visitors about the zoo

Population params:

$$\mu, \beta, \sigma^2$$

Sample params:

$$\hat{\mu}, \hat{\beta}, \hat{\sigma}^2$$ $$\bar{x}, \beta, s^2$$

Data visualization

Bar plots

Bar plots can show Categorical (nominal or ordinal) and numerical (discrete) data. Rust file

Box-and-whisker plots

Box-and-whisker plots can show numerical (interval or ratio) data. Rust file

Histograms

Histograms can show numerical data, they are just like bar plots but categories are binned or bucketed. Rust file

Pie charts

Pie charts can show nominal, ordinal or discrete data representing a percentage of the whole for each category in a visual way since they are contained in a circle. There is a condition on data to be able to use pie charts, the data must sum up 1 (or 100%). Rust file

Lines vs bars

Lines can be used when we have many bars for the sake of simplicity and clarity (better resolution) or in-graph comparisons.