• Mean: The "average" number; found by adding all data points and dividing by the number of data points.

• Median: The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).

• Mode: The most frequent number—that is, the number that occurs the highest number of times.


mean, median and mode

• Variance: The variance of the data is the average squared distance between the mean and each data value.

• Standard deviation: Standard deviation is calculated as the square root of the variance (the average squared deviation from the mean).



variance and standard deviation

Mean Squared Error is simply the variance of a potentially biased estimator $\hat{\theta}_m$ of the Expected Value or Mean $\theta$
$$MSE(\hat{\theta}_m) = \mathbb{E}((\hat{\theta}_m - \theta)^2)$$
$$ = Bias^2(\hat{\theta}_m) + Var(\hat{\theta}_m)$$

Mean Squared Error

In statistics, consistency is a property of an estimator where its probabilistic limit converges to the true underlying parameter value as the sample size approaches infinity ($$	ext{plim}_{mightarrow\infty}\hat{	heta}_m=	heta$$). When an estimator is consistent, accumulating more data guarantees that empirical estimates will eventually match the true theoretical probabilities.

Consistency of an Estimator

• mean

• median

• mode

• percentiles

• range

• variance

• standard deviation

• mean squared error

• consistency

University of Toledo

University of California, Davis

- Number of data points (instances)
- Attributes (variables)
- Types of attributes (variables)
- Number of attributes (variables)
- Statistical measures

Characteristics of a dataset

Most statistics and data science textbooks use the letter n to represent this number, and sometimes, they call it the number of observations.
The number of distinct data points depends on how the unit of data is defined in the dataset. In tabular datasets, this number is the number of rows.

Number of data points (instances)

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

Most statistics and data science textbooks use the letter p to represent this number, and sometimes, they call it the number of covariates.
In tabular datasets, this number is the number of columns.

Learn Before

Related

Learn After