CBSE Class 11 Statistics Chapter 7: Correlation NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 11 PDF

This chapter provides NCERT Solutions for Class 11 Statistics, focusing on Correlation. It covers the fundamental concepts of correlation, including the definition and properties of the correlation coefficient. Students will learn about the range of the correlation coefficient, understanding that it lies between -1 and +1. The solutions explain the interpretation of positive, negative, and zero correlation, indicating the direction and strength of the relationship between two variables. It also touches upon different methods to measure correlation, such as Karl Pearson's coefficient and Spearman's rank correlation, and when each is appropriate. These solutions are designed to help students grasp the nuances of correlation analysis, a key statistical tool for understanding relationships in economic data, and prepare effectively for their examinations.

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Quick info

Board	CBSE
Class	Class 11
Subject	Statistics (Economics)
Session	2026
Language	English
Type	NCERT Solutions
Chapter	7. Correlation

Chapter summary

Chapter 7 on Correlation in Class 11 Statistics NCERT Solutions delves into the concept of measuring the relationship between two variables. It clarifies the properties of the correlation coefficient, including its unitless nature and its range from -1 to +1. The solutions explain how to interpret positive, negative, and zero correlation, and differentiate between linear and non-linear relationships. It also briefly introduces different correlation measurement techniques like Karl Pearson's coefficient and scatter diagrams, highlighting their applicability.

Learning outcomes

Understand the concept and definition of correlation coefficient.
Identify the unitless nature of the correlation coefficient.
Determine the range of the simple correlation coefficient.
Interpret the meaning of positive, negative, and zero correlation.
Differentiate between linear and non-linear relationships based on correlation.
Recognize different measures of correlation and their applicability.

Topics covered

Paper topics

Correlation Coefficient
Unit of Correlation Coefficient
Range of Correlation Coefficient
Positive Correlation
Negative Correlation
Zero Correlation
Linear Relationship
Non-linear Relationship
Karl Pearson's Coefficient of Correlation
Spearman's Rank Correlation
Scatter Diagram
Association between Variables

Important topics

Range of Correlation Coefficient
Interpretation of Positive Correlation
Interpretation of Negative Correlation
Interpretation of Zero Correlation
Unitless Nature of Correlation Coefficient
Difference between Linear and Non-linear Relationships

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Questions and Solutions

Question 1

The unit of correlation coefficient between height in feet and weight in kgs is:

(i). Kg/feet

(ii). Percentage

(iii). non-existent

Solution: The correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two variables. It is a pure numerical value and does not carry any units of measurement. Therefore, the unit of the correlation coefficient between height in feet and weight in kgs is non-existent.

Answer: (iii). non-existent

Question 2

The range of simple correlation coefficient is:

(i). 0 to infinity

(ii). Minus one to plus one

(iii). Minus infinity to infinity

Solution: The simple correlation coefficient, often denoted by 'r', measures the linear association between two variables. Its value is always bounded between -1 and +1, inclusive. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and any value in between indicates the degree of linear association. Values outside this range suggest an error in calculation.

Answer: (ii). Minus one to plus one

Question 3

If $r_{xy}$ is positive, the relation between X and Y is of the type:

(i). When Y increases X increases

(ii). When Y decreases X increases

(iii). When Y increases X does not change

Solution: A positive correlation coefficient (

r_{xy} > 0

) indicates that the two variables, X and Y, tend to move in the same direction. This means that if the value of one variable increases, the value of the other variable also tends to increase, and conversely, if one decreases, the other tends to decrease. Option (ii) describes a negative correlation, and option (iii) suggests no correlation or a constant relationship.

Answer: (i). When Y increases X increases

Question 4

If $r_{xy} = 0$ , the variables X and Y are:

(i). Linearly related

(ii). Not linearly related

(iii). Independent

Solution: A correlation coefficient of zero (

r_{xy} = 0

) signifies the absence of a linear relationship between variables X and Y. It is important to note that this does not necessarily mean the variables are independent; they might still have a non-linear relationship. Independence implies zero correlation, but zero correlation does not always imply independence.

Answer: (ii). Not linearly related

Question 5

Of the following three measures, which can measure any type of relationship?

(i). Karl Pearson's coefficient of correlation

(ii). Spearman's rank correlation

(iii). Scatter diagram

Solution: While Karl Pearson's coefficient of correlation is widely used for measuring linear relationships and scatter diagrams provide a visual representation of relationships, Spearman's rank correlation is more versatile. It can measure both linear and non-linear relationships by analyzing the ranks of the data points. Therefore, Spearman's rank correlation is capable of measuring any type of relationship.

Answer: (ii). Spearman's rank correlation

Question 6

If precisely measured data are available, the simple correlation coefficient is:

(i). More accurate than rank correlation coefficient

(ii). Less accurate than rank correlation coefficient

(iii). As accurate as the rank correlation coefficient

Solution: When precisely measured data are available, both Karl Pearson's coefficient of correlation (which uses the actual values) and Spearman's rank correlation coefficient (which uses ranks derived from the values) can be applied. If the relationship is indeed linear, Karl Pearson's coefficient is generally considered more precise as it utilizes the full information from the data. However, if the data is ordinal or the relationship is monotonic but not strictly linear, Spearman's rank correlation is appropriate. In the context of measuring association from precisely measured data, assuming a linear relationship is expected, Karl Pearson's method is often preferred for its direct use of values. If the question implies comparing the accuracy in measuring the *same* type of relationship (linear), and assuming the data allows for it, both can be accurate. However, the source answer suggests they are equally accurate in their respective domains or when applied appropriately. A common interpretation is that if the data is interval/ratio and the relationship is linear, Karl Pearson's is the standard. If the data is ordinal or the relationship is monotonic, Spearman's is used. The source implies a scenario where both are applicable and yield comparable accuracy for the type of relationship they measure.

Answer: (iii). As accurate as the rank correlation coefficient

Question 7

Why is r preferred to covariance as a measure of association?

Solution: The correlation coefficient (r) is often preferred over covariance as a measure of association because covariance is sensitive to the units of the variables involved, making it difficult to compare the strength of association across different pairs of variables. The correlation coefficient, on the other hand, is a unitless measure, standardized by dividing the covariance by the product of the standard deviations of the two variables. This standardization allows for a consistent interpretation of the strength of the relationship, regardless of the original units of measurement, and its range is fixed between -1 and +1.

Common mistakes

Assuming correlation coefficient has units.
Confusing the range of correlation coefficient (e.g., 0 to infinity).
Misinterpreting zero correlation as complete independence.
Not understanding that correlation measures linear association primarily.

Revision tips

Memorize the range of the correlation coefficient (-1 to +1).
Clearly understand the implications of positive, negative, and zero correlation values.
Distinguish between correlation and causation.
Review the properties of the correlation coefficient, especially its unitless nature.

Practice MCQs

Q1. What is the unit of the correlation coefficient between height in feet and weight in kgs?

Q2. What is the possible range for the simple correlation coefficient?

Q3. If the correlation coefficient (r_xy) is positive, what does it imply about the relationship between variables X and Y?

Q4. What does a correlation coefficient (r_xy) of 0 indicate about the relationship between variables X and Y?

Q5. Which measure can be used to measure any type of relationship, including non-linear ones?

Frequently asked questions

What is the correlation coefficient?

The correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two variables. It is a pure number without any units.

What is the range of the correlation coefficient?

The simple correlation coefficient (r) can range from -1 to +1. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.

What does a positive correlation coefficient signify?

A positive correlation coefficient means that as one variable increases, the other variable also tends to increase. They move in the same direction.

What does a zero correlation coefficient signify?

A zero correlation coefficient (r=0) indicates that there is no linear relationship between the two variables. However, a non-linear relationship might still exist between them.

Does the correlation coefficient have any units?

No, the correlation coefficient is a unitless measure. It is a standardized value used to compare the degree of association between different pairs of variables.

How can these NCERT Solutions help in exam preparation?

These solutions provide clear explanations and rewritten answers for each question, helping students understand the core concepts of correlation, its properties, and interpretation, which are crucial for tackling exam questions effectively.

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