Master the Concept of Correlation for CBSE Class 11 Applied Mathematics. Learn Pearson's r, scatter diagrams, and interpretation with solved examples.
Correlation is a statistical measure that expresses the extent to which two variables are linearly related. It quantifies the strength and direction of the association between two quantitative variables, such as height and weight or advertising spend and sales. The value of the correlation coefficient, denoted by r, always lies in the closed interval [-1, 1].
Step 1: Identify variables X (study hours) and Y (test scores).
Step 2: Observe that as X increases, Y increases.
Step 3: Conclude that the correlation is positive, implying r > 0.
Answer: Positive Correlation.
The correlation coefficient r is a unit-free measure, meaning it remains unchanged by a change of origin or scale. If r = 1, there is a perfect positive linear relationship; if r = -1, there is a perfect negative linear relationship. If r = 0, the variables are uncorrelated, indicating no linear relationship exists between them.
Step 1: Given r(X, Y) = 0.8.
Step 2: Find r(2X + 5, 3Y - 2).
Step 3: Since constants do not affect r, the result is 0.8.
Answer: 0.8
A scatter diagram is a graphical representation of bivariate data where each pair (xᵢ, yᵢ) is plotted as a point on a Cartesian plane. The pattern of these points reveals the nature of the correlation. A tight cluster around a line indicates a strong correlation, while a dispersed cloud indicates a weak correlation.
Step 1: Plot points (1, 2), (2, 4), (3, 6).
Step 2: Observe points lie exactly on the line y = 2x.
Step 3: Conclude r = 1.
Answer: Perfect positive correlation.