Question

A _________ visually presents the nature of association without giving any specific numerical value.
(A) Karl Pearson’s coefficient of correlation
(B) Scatter diagram
(C) Spearman’s rank correlation
(D) All of these

Answer 1

Hint: In this question, we have to fill the blanks by choosing the required solution from the given particular options. We are going to solve this problem by using trial and error methods. For that, we need to first find the definition of all the options. Then we can easily find out the required solution to this question.

Complete step-by-step solution:
We need to find out the correct option which visually presents the nature of association without giving any specific numerical value.
Karl Pearson’s coefficient of correlation:
We know that Karl Pearson's Coefficient of Correlation is an extensively used mathematical method in which the numerical representation is applied to measure the level of relation between linear related variables. The coefficient of correlation is expressed by “r”.
\[r = \dfrac{{\sum {\left( {X - \overline X } \right)\left( {Y - \overline Y } \right)} }}{{\sqrt {\sum {{{\left( {X - \overline X } \right)}^2}} } \sqrt {{{\left( {Y - \overline Y } \right)}^2}} }}\]
Where,
\[\overline X \]= Mean of X variable
\[\overline Y \]= Mean of Y variable
Scatter diagram:
The scatter diagram is a technique used to examine the relationship between both the axis (X and Y) with one variable. In the graph, if the variables are correlated, the point will drop along a curve or line. A scatter diagram or scatter plot, is used to give an idea of the nature of relationship.
Spearman’s rank correlation:
In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter or as, is a nonparametric measure of rank correlation. It assesses how well the relationship between two variables can be described using a monotonic function.
\[\rho = 1 - \dfrac{{6\sum {{d_i}^2} }}{{n\left( {{n^2} - 1} \right)}}\]
\[\rho \] = Spearman’s rank correlation coefficient
\[{d_i}\]= Difference between the two ran of each observation
n = Number of observations
Thus the only option which visually presents the nature of association without giving any specific numerical value is Scatter diagram.

$\therefore $ Option (B) is the correct option.

Note: Trial and error is a fundamental method of problem solving. It is characterized by repeated, varied attempts which are continued until success, or until the practice stops trying. This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory. However, there are intermediate methods which for example, use theory to guide the method, an approach known and guided empiricism.