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NCERT Solutions

Class 11

Statistics

Chapter 6 Correlation

CBSE Class 11 Statistics Chapter 6 Correlation – NCERT Solutions 2025-26

Q: 1. How do you solve questions on Karl Pearson's coefficient of correlation from NCERT Class 11 Statistics, Chapter 6?

To solve problems using Karl Pearson's method as per the NCERT textbook, you must follow a precise step-by-step process to ensure accuracy and full marks.Step 1: Calculate the mean for both variable series, X (X̄) and Y (Ȳ).Step 2: Find the deviation of each value from its respective mean (x = X - X̄ and y = Y - Ȳ).Step 3: Square these deviations (x² and y²) and find their sums (Σx² and Σy²).Step 4: Multiply the deviations of both series (xy) and find the sum (Σxy).Step 5: Apply the formula: r = Σxy / √ (Σx² * Σy²).Step 6: Interpret the final value of 'r' to describe the relationship between the variables.

Download Free PDF of Correlation for Class 11 Statistics Chapter 6

If you are preparing for your Class 11 Statistics board exam, a strong grasp of correlation is essential. Chapter 6, “Correlation,” explores how two variables are linked using statistical tools like scatter diagrams, Karl Pearson’s coefficient, and Spearman’s rank method. These concepts commonly appear in board exams and together hold a 12-mark weightage in your Statistics and Probability Unit.

Table of Content

Many students search for “correlation class 11 notes” or “important questions of correlation class 11” when revising key definitions or solving exam-type questions. With semantic topics such as types of correlation and calculation-based questions covered, this content helps in interpreting correlation coefficients and prevents confusion between positive, negative, and zero relationships.

Each solution on Vedantu is carefully aligned with the latest CBSE syllabus, empowering you to overcome exam anxiety and build lasting confidence in correlation analysis.

Questions Included in NCERT Solutions for Class 11 Statistics for Chapter 6

The NCERT solutions come in a question-answer format. The answers have been drafted, keeping in mind the marking scheme of the CBSE exam. Referring to these answers help a student acquire an idea about how to write their answers in a proper manner.

Class 11 Statistics Chapter 6 Correlation could be a tricky chapter if not understood in detail. Thus, students must put extra attention to this particular chapter in Statistics. There are 18 total questions included in the exercise of this chapter. Here is a gist of the questions included in the NCERT Solutions of the ‘Correlation’ chapter:

1: The first question in this chapter carries three options provided for this question, from which students need to select the correct answer. Here, the right answer would be ‘non-existent’, because the correlation coefficient does not have a unit. It is represented as 'r' and happens to be a pure number.

2: The second question in NCERT Solutions for Class 11 Statistics for Chapter 6 asks about the simple correlation coefficient’s range. Here the three options are ‘0 to infinity’, ‘-1 to +1’, and ‘minus infinity till infinity’. The range of correlation coefficient is, however, -1 to +1. Any value of it out of this range is invalid.

3: The 3rd question in Class 11 NCERT solutions Statistics ch 6 asks what the positive value of rXY denotes about the relationship between X and Y. The correct answer to this question is that when Y increases, X increases as well. If the value of r is positive, both the variables move in a similar direction. For example, if the market price of tea increases, the demand for coffee also increases simultaneously as it substitutes tea.

4: The 4th question is almost similar to the previous one. It asks about the relationship between X and Y if the value of rXY is 0. If the value is 0, it denotes that X and Y are uncorrelated. This means that there is an absence of a linear relationship between the two variables.

5: This question gives three options, out of which students have to select which one measures all types of relationships. The answer here would be ‘scatter diagram’. Scatter diagram is not just limited to linear relations. It provides a visual representation of any relationship between two variables. The other two options- ‘Karl Pearson’s coefficient’ and ‘Spearman’s rank correlation’, both measure linear relationships.

6: The answer to the 6th question in NCERT solutions Class 11 Statistics Chapter 6 is that the simple correlation coefficient should be more accurate than the rank correlation coefficient.

7: The question here is ‘why r is preferred over covariance as a measure of association?’ Correlation coefficient as well as covariance measure the degree of the linear relationship between two variables. However, the correlation coefficient is still preferred to covariance because of certain reasons. The NCERT Solutions for Class 11 Statistics for Chapter 6 lists two reasons in this context.

8: The 8th question is whether r can lie out of the range of -1 and +1, depending upon the nature of data. But the answer here will be 'no' because the value of the correlation coefficient can never lie out of this range. Any value out of this range indicates an error or invalidity.

9: The 9th question is ‘Does correlation imply causation?’ The answer in this question would again be a ‘no’. Correlation does not denote causation. It measures co-variation. Correlation gives an idea of the intensity and direction of change in a variable when the correlated variable changes.

10: The 10th question in NCERT Solutions for Class 11 Statistics for Chapter 6 is a comparison between rank correlation and simple Correlation. It asks students to identify which out of the two is comparatively more precise. In the NCERT solutions, you will get three points which justify the precision of rank correlation over simple Correlation.

11: This question asks whether zero Correlation means independence? Zero Correlation, however, does not imply independence. Rather, it denotes that the two variables are uncorrelated and share no linear relation between them.

12: The question here is if the simple correlation coefficient can measure any sort of relationship. But a simple correlation coefficient cannot measure all types of relationships. It can only measure linear relationships.

13: This question asks students to list a few variables where accurate measurement is difficult. The answer contains two points with this respect. It is difficult for qualitative aspects like honesty, beauty, intelligence, and so on. It is difficult also when it comes to measuring subjective aspects like development, poverty, etc.

14: The 14th question in NCERT Solutions for Class 11 Statistics for Chapter 6 asks you to interpret all the values of r as 1, -1, and 0. Each interpretation has been detailed elaborately in the respective answer.

15: This question asks students to differentiate between Pearson’s correlation coefficient and rank correlation coefficient. There are four points on which these two can be differentiated.

Questions 16, 17, and 18 are numerical sums based on calculating the correlation coefficient.

Every answer in the NCERT Solutions for Class 11 Statistics for Chapter 6 has been presented in a student-friendly manner. They can grasp the concept at one go and remember it for longer.

CBSE Class 11 Statistics Chapter 6 Other Study Materials

S. No	Important Study Material Links for Chapter 6 Correlation
1.	Class 11 Correlation Important Questions
2.	Class 11 Correlation Revision Notes

Chapter-wise NCERT Solutions for Class 11 Statistics

S. No	NCERT Solutions Class 11 Statistics Chapter-wise List
1	Chapter 1 - Introduction to Statistics Solutions
2	Chapter 2 - Collection of Data Solutions
3	Chapter 3 - Organisation of Data Solutions
4	Chapter 4- Presentation of Data Solutions
5	Chapter 5 - Measures of Central Tendency Solutions
6	Chapter 7 - Index Numbers Solutions
7	Chapter 8 - Use of Statistical Tools Solutions

Important Related Links for CBSE Class 11 Statistics

S.No	Study Material for Class 11 Economics
1.	CBSE Class 11 Economics NCERT Books
2.	CBSE Class 11 Economics Important Questions
3.	CBSE Class 11 Economics Sample Papers
4.	CBSE Class 11 Economics NCERT Solutions
5.	CBSE Class 11 Economics Sandeep Garg Solutions
6.	CBSE Class 11 Economics Notes
7.	CBSE Class 11 Economics Syllabus

FAQs on CBSE Class 11 Statistics Chapter 6 Correlation – NCERT Solutions 2025-26

1. How do you solve questions on Karl Pearson's coefficient of correlation from NCERT Class 11 Statistics, Chapter 6?

To solve problems using Karl Pearson's method as per the NCERT textbook, you must follow a precise step-by-step process to ensure accuracy and full marks.

Step 1: Calculate the mean for both variable series, X (X̄) and Y (Ȳ).
Step 2: Find the deviation of each value from its respective mean (x = X - X̄ and y = Y - Ȳ).
Step 3: Square these deviations (x² and y²) and find their sums (Σx² and Σy²).
Step 4: Multiply the deviations of both series (xy) and find the sum (Σxy).
Step 5: Apply the formula: r = Σxy / √ (Σx² * Σy²).
Step 6: Interpret the final value of 'r' to describe the relationship between the variables.

2. What is the correct method for calculating Spearman's Rank Correlation Coefficient for NCERT exercises?

Spearman's Rank Correlation is used for qualitative data or when ranks are given. The correct method involves these steps:

Step 1: Assign ranks (R₁) to the first variable (X) and ranks (R₂) to the second variable (Y). If ranks are tied, assign the average rank to each tied item.
Step 2: Calculate the difference between the ranks for each pair of observations (D = R₁ - R₂).
Step 3: Square each difference (D²) and then find the sum of these squared differences (ΣD²).
Step 4: Apply the formula: rₛ = 1 - [6ΣD² / n(n² - 1)], where 'n' is the number of pairs of observations.
Step 5: If ranks are tied, a correction factor is added to the ΣD² value before using the main formula.

3. What are the key formulas from Chapter 6 that are essential for solving all the NCERT exercise questions?

To successfully solve all questions in the NCERT Chapter 6 exercises, you must be proficient with these three primary methods and their formulas:

Karl Pearson's Coefficient (r): Used for quantitative data. The main formula is r = Σxy / √ (Σx² * Σy²), where x and y are deviations from the mean.
Spearman's Rank Correlation (rₛ): Used for qualitative data or ranked data. The formula is rₛ = 1 - [6ΣD² / n(n² - 1)].
Scatter Diagram: This is a graphical method and does not have a formula. It requires plotting data points on a graph to visually determine the direction and strength of the correlation.

4. How do the NCERT solutions for Chapter 6 cover all the exercises provided in the textbook?

Comprehensive NCERT solutions for Class 11 Statistics Chapter 6 provide detailed, step-by-step answers for all 18 questions listed in the chapter-end exercise. This includes theoretical questions, interpretation-based problems, and numerical sums requiring calculations for both Karl Pearson's and Spearman's methods, ensuring complete preparation as per the CBSE 2025-26 syllabus.

5. Why is the correlation coefficient (r) considered a better measure of association than covariance when solving problems?

The correlation coefficient (r) is preferred over covariance because it is a standardised, unit-free measure. While covariance indicates the direction of the linear relationship, its value is affected by the units of the variables (e.g., kg, cm). In contrast, 'r' always lies between -1 and +1, making it a pure number that allows for easy comparison of the strength of linear relationships between different pairs of variables, regardless of their original units.

6. When solving an NCERT problem, how do you interpret the resulting correlation coefficient values of +1, -1, and 0?

The interpretation of the correlation coefficient 'r' is crucial for the final answer in NCERT solutions:

r = +1: This indicates a perfect positive correlation. It means that the two variables move in the same direction at a constant proportion. For every unit increase in one variable, the other increases by a fixed proportion.
r = -1: This indicates a perfect negative correlation. The variables move in opposite directions at a constant proportion. For every unit increase in one, the other decreases by a fixed proportion.
r = 0: This indicates no linear correlation. There is no straight-line relationship between the two variables.

7. If an NCERT question results in a zero correlation, does this imply the variables are independent? Explain the correct interpretation.

No, a correlation coefficient of zero (r=0) does not necessarily mean the variables are independent. It only implies the absence of a linear relationship between them. It is possible for two variables to be strongly related in a non-linear way (e.g., a U-shaped or circular relationship) and still have a correlation coefficient of zero. Therefore, the correct interpretation is that the variables are uncorrelated, not that they are independent.

8. What are the common mistakes to avoid while solving numerical problems on correlation from the NCERT textbook?

Students often make a few common errors when solving correlation sums. To ensure accuracy, you should avoid:

Calculation Errors: Simple mistakes in calculating means, deviations (x and y), or their squares (x² and y²).
Formula Mix-up: Confusing the formula for Karl Pearson's method with Spearman's rank correlation.
Sign Errors: Forgetting to include the correct positive or negative sign when calculating deviations or the final coefficient.
Ranking Errors: Incorrectly assigning ranks or failing to use the correction factor for tied ranks in Spearman's method.
Interpretation Mistakes: Stating that r=0 means independence, or failing to properly explain what the calculated 'r' value signifies.

9. Where can I find reliable, step-by-step NCERT Solutions for Class 11 Statistics Chapter 6 for the 2025-26 session?

You can find reliable and accurate NCERT Solutions for Class 11 Statistics Chapter 6 on trusted educational platforms like Vedantu. These solutions are prepared by subject matter experts and are fully aligned with the latest CBSE 2025-26 syllabus. They provide detailed, step-by-step explanations for every question in the exercise, helping you understand the correct methodology for scoring full marks in your exams.