NCERT Solutions for Class 11 Statistics Chapter 7 - Correlation
The National Council of Educational Research and Training (NCERT), even since its establishment in 1961, has been working to enhance the quality and structure of education in India. The council develops textbooks, learning materials, training models, and so on to help students with their academics. NCERT solutions are also a step towards assisting students. NCERT Solutions for Class 11 Statistics for Chapter 7 is one of them. The solution includes precise answers to the textbook questions. All the NCERT solutions are also available in PDF format.
Statistics is a crucial subject when it comes to the Class 11 curriculum. Students need to be attentive and practise regularly to score well in this subject. The 7th chapter in the Class 11 Statistics chapter is Correlation. Correlation can be defined as the relationship between two variables over a given time period. It measures co-variation. Students can strengthen their textbook study of this chapter through NCERT solutions. To find the soft copy of Class 11 NCERT solutions Statistics Ch 7, you can download the Vedantu App.
The NCERT Solutions for Class 11 Statistics Chapter 7 PDF will be uploaded soon.
Questions Included in NCERT Solutions for Class 11 Statistics for Chapter 7
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 7 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 7 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 7 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 7 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 7 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 7 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 7 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 7 has been presented in a student-friendly manner. They can grasp the concept at one go and remember it for longer.
FAQs (Frequently Asked Questions)
1. What is Pearson's Correlation Coefficient?
Pearson’s correlation coefficient is used in linear regression. It is used for measuring the strength of the association between two variables - The 7th seventh chapter in the Class 11 Statistics syllabus details this topic with examples.
2. How Many Questions are There in the NCERT Solutions for Class 11 Statistics for Chapter 7?
The 7th chapter in Class 11 NCERT Statistics solutions includes eighteen questions in total. These questions include objective, subjective, as well as numerical problems.
3. How Many Sums are There in NCERT Solutions Class 11 Statistics Chapter 7?
There are three sums in the 7th chapter of NCERT solutions for Class 11 Statistics. Question 16, 17, and 18 are numerical problems.
4. What is correlation Class 11 Statistics Chapter 7?
Correlation in Class 11 is defined as a tool used in statistics for studying the relationship between two variables, for example, change in price leads to change in quantity demanded. Correlation also gives information about the measure of direction and intensity of the relationship between the two variables. It is not the cause and effect relation. Correlation may be classified into two types that are positive and negative correlation.
5. How do you find the Correlation Coefficient for Class 11 Statistics?
Karl Pearson’s Coefficient Correlation can be calculated as the product of moment correlation and simple correlation coefficient. It is a quantitative method of calculating the correlation coefficient. The correlation coefficient can be denoted by the letter V. Students can check the NCERT Solutions for Statistics Class 11 Chapter 7 from the vedantu website or the app. All the solutions are available in the PDF file and students can download the file free of cost for proper understanding of the concepts.
6. How do you solve for Correlation Coefficients?
The Correlation Coefficient can be calculated by two methods. The Actual Mean method and the Assumed Mean method. When the calculations are difficult, we can use the step deviation method for reducing the calculations. Another method that can be used is Spearman’s rank correlation method. It can also be used for calculating the coefficient of correlation of qualitative variables such as bravery, wisdom, beauty, ability, virtue, etc. This method got its name because it was given by the British Psychologist C.E. Spearman.
7. What is the range of simple correlation coefficient Class 11 Statistics?
Correlation can be defined as the measure or a tool that helps to determine the strength and the direction of the relationship between two variables, X and Y. The range of a correlation coefficient is from -1 to 1. Students can check the vedantu’s NCERT Solutions. The Solutions are given by expert teachers in a simple and easy-to-understand language. Students can use the notes for their exam preparation.
8. Does correlation imply causation?
No, correlation does not imply causation. Correlation helps to measure co-variation and not causation. The correlation only helps to understand the idea of the direction and intensity of change in a variable when the correlated variable changes. Correlation between two variables only helps to know that when the value of one variable changes in one direction the value of the other variable may change in the same direction or the opposite direction.