NCERT Solutions for Class 11 Statistics Chapter 7 - Correlation

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.