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Class 11 Economics Short Questions with Answers: Correlation - 2

Q: 2. How is correlation coefficient calculated?

Ans. The correlation coefficient, denoted by 'r,' is calculated using the formula r = (Σ((xi - x̄)(yi - ȳ))) / √(Σ((xi - x̄)^2) * Σ((yi - ȳ)^2)), where xi and yi are the individual values of the two variables, x̄ and ȳ are their respective means, and Σ represents the sum of the values. The resulting coefficient ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

Q.16. What is the nature of correlation if the value of r is –1?
Ans. When r is –1, there is perfect negative correlation between variables.

Q.17. What is the value of r if the two variables are not related?
Ans. When the two variables are not related, r = 0.

Q.18. State the merits of Karl Pearson’s correlation coefficient.
Ans. The merits of Karl Pearson’s correlation coefficient are:
(i) It is a real measure of correlation coefficient as it is based on arithmetic mean and standard deviation.
(ii) It finds out not only the direction but also the actual degree of correlation between variables.

Q.19. What are the demerits of Karl Pearson’s correlation coefficient.
Ans. The demerits of Karl Pearson’s correlation coefficient are:
(i) The values of correlation coefficient are unduly affected by extreme values.
(ii) The assumption that there is a linear relation between variables is not always true.
(iii) The analysis of correlation coefficient requires a lot of care as there is a possibility of misinterpretation of results.
(iv) It involves long mathematical calculation and hence, is a time-consuming method.

Q.20. How does Spearman’s rank correlation measure relation between variables?
Ans. Spearman’s rank correlation measures the linear relation between ranks assigned to individual items according to their attributes.

Q.21. Name some qualitative variables.
Ans. Examples of qualitative variables include beauty, wisdom, bravery, dedication, honesty, etc.

Q.22. Who developed Spearman’s rank correlation?
Ans. Spearman’s rank correlation was developed by British psychologist C.E. Spearman.

Q.23. When is rank correlation preferred to Pearsonian coefficient?
Ans. Rank correlation is preferred to Pearsonian coefficient when extreme values are present.

Q.24. What are the merits of rank correlation coefficient?
Ans. The merits of rank correlation coefficient are:
(i) It is easier to calculate and understand correlation using this method.
(ii) This method is the most appropriate for the calculation of correlation in case of qualitative and irregular facts.
(iii) This method can be employed for finding correlation even when the actual data is not given. Correlation can be found by simply using the ranks assigned to the values.

Q.25. Write the demerits of rank correlation coefficient.
Ans. The demerits of rank correlation coefficient are:
(i) This method is not so definite.
(ii) This method cannot be used when number of items is very high.
(iii) This method is applicable only to individual series and not for frequency distributions.

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FAQs on Class 11 Economics Short Questions with Answers: Correlation - 2

1. What is correlation and why is it important in statistics?

Ans. Correlation is a statistical measure that indicates the degree to which two variables are related. It measures the strength and direction of the linear relationship between the variables. Correlation is important in statistics as it helps in understanding the relationship between variables, making predictions, and analyzing the dependency between different factors.

2. How is correlation coefficient calculated?

Ans. The correlation coefficient, denoted by "r," is calculated using the formula r = (Σ((xi - x̄)(yi - ȳ))) / √(Σ((xi - x̄)^2) * Σ((yi - ȳ)^2)), where xi and yi are the individual values of the two variables, x̄ and ȳ are their respective means, and Σ represents the sum of the values. The resulting coefficient ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

3. Can correlation imply causation?

Ans. No, correlation does not imply causation. Correlation only shows the relationship between variables but does not determine if one variable causes the change in another. It is possible to have a strong correlation between two variables, but it doesn't necessarily mean that one variable is causing the change in the other. Causation requires further research and analysis to establish a cause-and-effect relationship.

4. What are the limitations of correlation analysis?

Ans. Correlation analysis has certain limitations. Firstly, it only measures the linear relationship between variables and may not capture other types of relationships. Secondly, correlation does not provide information about the strength of the relationship in terms of magnitude. Additionally, outliers or extreme values can significantly influence the correlation coefficient. Lastly, correlation does not provide information on the direction of the relationship or whether it is influenced by other variables.

5. How can correlation be interpreted?

Ans. Correlation can be interpreted based on the value of the correlation coefficient (r). If r is close to +1, it indicates a strong positive correlation, meaning that as one variable increases, the other variable tends to increase as well. A value close to -1 indicates a strong negative correlation, where one variable increases while the other decreases. A value close to 0 suggests no or weak correlation, meaning the variables are unrelated or have a weak linear relationship. The magnitude of r also indicates the strength of the correlation, with larger values representing stronger relationships.

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