Descriptive Statistics¶
Descriptive statistics aims to describe a given data set visually and through metrics. There is no uncertainty in descriptive statistics! It is a crucial step in every exploratory analysis as we get a better feeling for the data, its characteristics and relationships.
In descriptinve statistics, we do:
observe data
apply models and metrics to the data
describe and explain the outcome
There is also inferential statistics where you would predict values using a statistical model.
Random Variables¶
In statistics, a random variable or variable represents the input or output data of a statistical model. In practice, each column of a data set can be regarded as the observed values of a random variable.
A variable can be described by a probability distribution function, even if that function is not known. In practice this means that you can talk and write about a variable even if you have not collected any data yet.
Hint
If you want to avoid ambiguity with the very different concept of variables in programming, use the term random variable.
Observation¶
An observation is an instance of data that you have. E.g. a row in a table.
Population¶
A population contains every subject that is of interest in order to answer a certain question. In practice, if you know the population, it means that you have collected all data that exists (good).
Sample¶
A sample consists of one or more observations. It is a random or non-random subset of a population. In practice having a sample means you are working with incomplete data.
Types of Variables¶
Categorical¶
Categorical variables (also called nominal variables) have values or labels that do not follow a natural ordering.
Sometimes we encode the labels of categorical variables as numbers.
Although, in that case, the data type of these variables is int or float, mathematical operations
(addition, multiplicaton, …) shouldn’t be applied to it.
Examples:
Location (Berlin, Johannesburg, …)
Nationality
Postal Codes (54296, 50679, …)
Ordinal¶
Ordinal or ranked variables have values that follow a natural order. However, the difference between the values is not measurable. As with categorical variables we often encode this kind of data with numeric values.
Examples:
Movie Ratings (5 Stars, …, 1 Star)
Evaluation (‘Very Good’, ‘Good’, …, ‘Awful’)
Month of the year (1, 2, 3, …, 12)
Numerical¶
Numerical (scalar) variables have values with a natural ordering and the distance between two values is interpretable. Hence, we can say “this value is twice as large as the other value”. Numerical variables can be both integer numbers or floating point numbers.
Examples:
Height in cm (186, 150)
Age in years
Price in $
Discrete Variables¶
Discrete variables have a finite number of possible values. Ordinal and categorical variables are always discrete. Note, that metric variables can often be modeled as either discrete or continuous.
Examples:
Number of books delivered by Amazon each day
Number of rainy days per year
Movie Ratings (5 Stars, …, 1 Star)
Continuous Variables¶
Continuous variables have a theoretically infinite number of possible values.
Examples:
distance between two cities
Height (in cm)
Age (in years)
A few more types¶
Here are some extra types of variables. To many of these, special rules apply
binary numbers
dates and times (depends on how exactly the time is encoded)
time series (a value over time)
angles, longitude and latitude (they are circular)
text
images
hashes