Worksheet Solutions: Correlation | Economics Class 11 - Commerce PDF Download

Multiple Choice Questions

Assertion–Reasoning based  MCQs

Case Study Questions Measures of Correlation

Short Answer Type Questions 

Q1: Why is ‘r’ preferred to covariance as a measure of association?
Ans: Both, correlation coefficient and covariance measure the degree of linear relationship between two variables but correlation coefficient is generally preferred to covariance.
It is due to the following reasons
(i) The correlation coefficient (r ) has no unit.
(ii) The correlation coefficient is independent of origin as well as scale.

Q2: What do you understand by ‘spurious’ or ‘non-sense’ correlation?
Ans: If there is no evident or sensible connection between two variables, then the correlation between these variables is said to be spurious, non-sense or chance correlation. For example, correlation between rainfall recorded and production of steel.
These two variables are not connected by any way. So,the correlation between these variables is said to be spurious.

Q3: Give the advantages of Karl Pearson’s coefficient of correlation.
Ans: The advantages of Karl Pearson’s coefficient of correlation are
(i) Karl Pearson’s coefficient of correlation indicates the relationship as positive or negative and thus direction of the relationship can be ascertained.
(ii) This measure gives summarised and precise quantitative figure of correlation which can be interpreted easily and can provide meaningful results.
(iii) This coefficient of correlation indicates the direction and also the degree of relationship between the two variables. It shows whether the relationship is high, moderate or low.

Q4: List some variables where accurate measurement is difficult.
Ans: Accurate measurement is difficult in case of
(i) Qualitative variables such as beauty, intelligence,honesty, etc.
(ii) It is also difficult to measure subjective variables such as poverty, development, etc, which are
(iii) Where the cause and effect relationship is not known.

Q5: Interpret the values of r as 1, –1 and 0.
Ans: (i) If r = 0, the two variables are uncorrelated. There is no linear relation between them. However, other types of relation may be there and hence thevariables may not be independent.
(ii) If r = 1, the correlation is perfectly positive. The relation between them is exact in the sense that if one increases,the other also increases in the same proportion and if one decreases, the other also decreases in the same proportion.
(iii) If r = –1, the correlation is perfectly negative. The relation between them is exact in the sense that if one increases, the other decreases in the same proportion and if one decreases, the other increases in the same proportion.

Q6: Can r lie outside the −1 and 1 range depending on the type of data?
Ans: No, the value of the correlation coefficient lies between minus one and plus one i.e., −1 £ r £ 1. If the value of r is outside this range in any type of data, it indicates error in calculation as in between two or more variables, there can be either a perfect or an imperfect relationship. A perfect relationship is indicated by –1 or 1 and imperfect relationships are indicated by a value between –1 and 1,excluding 0.

Q7: Give the disadvantages of Karl Pearson’s coefficient of correlation.
Ans: The disadvantages of Karl Pearson’s coefficient of correlation are
(i) The value of coefficient is affected by extreme items.
(ii) The calculation process consumes a lot of time.
(iii) Correlation coefficient needs very careful interpretation, otherwise it may be misinterpreted.