Quantitative data is referred to as Continuous or Discrete data because it comprised of numerical data. This data is commonly stored in data types of Integer, Float, and Double. When using Quantitative data for Statistical learning it is often used in regression problems to predict a numerical output such as percent increase or decrease. This data is a an objective measurement.

Quantitative Data 

Qualitative data is often refered to as categorical data becuase it consists of non-numerical data. The most commoan data types it is stored in is often Boolean or Text. This data is often collected through conducting interveiws or observations. Qualitative data is often more subjective than quantitve data. When using Qualitative data for Statistical learning, it is often within a classification problem. 

Qualitative Data 

Data points most fall into one of two categories:
- Qualitative
- Quantitative

University of Michigan - Ann Arbor

A datapoint, instance, sample, or observation, is a unit of data in a dataset.
When datasets are tabular, $x_{ij}$ usually represents the value of the $j$th variable (attribute) in the $i$th data point, where $i=1,2,...,n$ indicates the index of the variable and $j=1,2,...,p$ identifies the variable. This way, a dataset can be represented as an $n\times p$ matrix X, where the row (or vector) $x_i$ represents a datapoint that consists of the $p$ values of $x_{i1}, x_{i2}, x_{i3}, \dots , x_{ip}$ corresponding to each variable.
$$X=\begin{bmatrix}
    x_{11} & x_{12} & x_{13} & \dots  & x_{1p} \\
    x_{21} & x_{22} & x_{23} & \dots  & x_{2p} \\
    \vdots & \vdots & \vdots & \ddots & \vdots \\
    x_{n1} & x_{n2} & x_{n3} & \dots  & x_{np}
\end{bmatrix}
=\begin{bmatrix}
    x_1^T \\
    x_2^T \\
    \vdots \\
    x_n^T \\
\end{bmatrix}$$ 

Datapoint

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Most textbooks represent vectors (columns) of a tabular dataset $X$ as:
$$X_j=\begin{bmatrix}
    x_{1j} \\
    x_{2j} \\
    x_{3j} \\
    \vdots \\
    x_{nj} \\
\end{bmatrix}$$
So, the dataset can be represented as $$X=\begin{bmatrix}
    X_{1} & X_{2} & X_{3} & \dots  & X_{p}
\end{bmatrix}$$.

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