Answered

What is one of the most widely used measures for evaluating similarity with numerical variables? It is defined as the length of a straight line between two observations.


AAlgebraic manipulation
BGeometric calculations
CManhattan distance
DEuclidean distance

Verified Answer :

Final answer:

The most widely used measure for evaluating similarity with numerical variables is the Euclidean distance. It represents the straight line distance between two observations in a coordinate space. An example illustrates its calculation by finding the distance between two points A(1, 2) and B(4, 6), which equals 5 units.


Explanation:

Understanding Similarity Measures: Euclidean Distance

One of the most widely used measures for evaluating similarity between numerical variables is the Euclidean distance. It is defined as the length of a straight line between two observations in a multi-dimensional space.

The Euclidean distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

For example, consider two points in a two-dimensional space, A(1, 2) and B(4, 6). The Euclidean distance between these two points can be calculated as follows:

  1. Calculate the differences: (4 - 1) = 3 and (6 - 2) = 4
  2. Square the differences: 3² = 9 and 4² = 16
  3. Add the squares: 9 + 16 = 25
  4. Take the square root: √25 = 5

Thus, the Euclidean distance between points A and B is 5 units. This measure is essential in various applications, such as clustering and classification in data analysis.


Learn more about Euclidean distance here:

https://brainly.com/question/43322533


Related Questions