# NCERT Notes for Class 11 statistics Chapter 7 Measures of Correlation

## Class 11 statistics Chapter 7 Measures of Correlation

NCERT Notes for Class 11 statistics Chapter 7 Measures of Correlation, (Statistics) exam are Students are taught thru NCERT books in some of state board and CBSE Schools.  As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation.  Students need to clear up those exercises very well because the questions withinside the very last asked from those.

Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions.  To assist students, solve all of the questions and maintain their studies without a doubt, we have provided step by step NCERT Notes for the students for all classes.  These answers will similarly help students in scoring better marks with the assist of properly illustrated Notes as a way to similarly assist the students and answering the questions right.

## CORRELATION

What Does Correlation Measure?

• Correlation studies and measures the direction and intensity of relationship among variables.
• Correlation measures covariation, not causation.
• Correlation should never be interpreted as implying cause and effect relation.

## Types of Correlation

• Correlation is commonly classified into negative and positive correlation.
• The correlation is said to be positive when the variables move together in the same direction.
• The correlation is negative when the variables move in opposite directions.

TECHNIQUES FOR MEASURING CORRELATION

Three important tools used to study correlation are

• Scatter diagrams
• Karl Pearson’s coefficient of correlation
• Spearman’s rank correlation.

Karl Pearson’s coefficient of correlation and Spearman’s rank correlation measure linear relationship among variables.

The scatter diagram gives a visual presentation of the relationship and is not confined to linear relations

• Scatter diagram visually presents the nature of association without giving any specific numerical value.
• A numerical measure of linear relationship between two variables is given by Karl Pearson’s coefficient of correlation. A relationship is said to be linear if it can be represented by a straight line.
• Spearman’s coefficient of correlation measures the linear association between ranks assigned to individual items according to their attributes. Attributes are those variables which cannot be numerically measured such as intelligence of people, physical appearance, honesty, etc.

## Scatter Diagram

• A scatter diagram is a useful technique for visually examining the form of relationship, without calculating any numerical value.
• In a scatter diagram the degree of closeness of the scatter points and their overall direction enable us to examine the relationship.
• If all the points lie on a line, the correlation is perfect and is said to be in unity.
• If the scatter points are widely dispersed around the line, the correlation is low.
• The correlation is said to be linear if the scatter points lie near a line or on a line.

## Karl Pearson’s Coefficient of Correlation

• Karl Pearson’s coefficient of correlation should be used only when there is a linear relation between the variables.
• When there is a non-linear relation between X and Y, then calculating the Karl Pearson’s coefficient of correlation can be misleading.

## Properties of Correlation Coefficient

• A negative value of r :(r = value of the correlation co-efficient) indicates an inverse relation between variables.
• If r is positive the two variables move in the same direction.
• If r = 0 the two variables are uncorrelated. There is no linear relation between them. If r = 1 or r = –1 the correlation is perfect and there is exact linear relation.
• A high value of r indicates strong linear relationship. Its value is said to be high when it is close to +1 or –1.
• A low value of r (close to zero) indicates a weak linear relation.

## Spearman’s rank correlation

Spearman’s rank correlation was developed by the British psychologist C.E. Spearman. It is used in the following situations:

• It is used when we are dealing with things such as fairness, honesty or beauty.
• It is used when assessment is made using rank.
• Spearman’s rank correlation coefficient can be used in some cases where there is a relation whose direction is clear but which is nonlinear.
• Spearman’s correlation coefficient is not affected by extreme values.