**Class 11 statistics Chapter 7 Measures of Correlation**

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

**Class 11 statistics Chapter 7 Measures of Correlation**

## 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.