Q.1. Define correlation.
Ans: Correlation is a statistical measure that indicates the direction and degree of relationship between two or more variables. It shows whether and how strongly variables move together. Correlation does not by itself prove that one variable causes the other to change; it only shows how they vary with respect to each other.
Q.2. How many types of correlation are there?
Ans: Correlation is mainly classified into two basic types - positive correlation and negative correlation. In addition, there may be zero (no) correlation when no clear relationship exists between variables.
Q.3. What happens when there is a negative correlation between variables X and Y?
Ans: When there is negative correlation between variables X and Y, as X increases, Y tends to decrease, and as X decreases, Y tends to increase. In simple terms, the variables move in opposite directions. For example, the price of a commodity and the quantity demanded often show a negative correlation: when price rises, demand usually falls.
Q.4. Give an example of positive correlation.
Ans: Example of positive correlation: temperature and sale of cold drinks. As temperature rises, sales of cold drinks tend to rise; when temperature falls, sales tend to fall too.
Q.5. List the various techniques of measuring correlation.
Ans: The various techniques of measuring correlation are:
(i) Scatter diagram - a graphical method that plots paired observations to show the pattern of relationship.
(ii) Karl Pearson's Coefficient of Correlation - a numerical measure (denoted by r) that quantifies the strength and direction of a linear relationship.
(iii) Spearman's Rank Correlation - a method used when data are ordinal or when we compare ranks rather than raw values.
Q.6. Explain the types of correlation.
Ans: Correlation is mainly classified into two types - positive correlation and negative correlation.
(i) Positive Correlation: Two variables move in the same direction. That is, when one variable increases, the other also increases; when one decreases, the other decreases. Example: income and consumption expenditure.
(ii) Negative Correlation: Two variables move in opposite directions. That is, when one variable increases, the other decreases; when one decreases, the other increases. Example: price of a good and quantity demanded (in many cases).
Q.7. Discuss the importance of correlation.
Ans: Importance of correlation:
(i) Formation and Testing of Economic Laws: Correlation helps to study the relationship between economic variables and to test economic principles. For example, it can be used to check the relationship implied by the law of demand.
(ii) Studying Economic Problems: Correlation assists in identifying relationships that may explain an economic problem, for instance, whether inflation is related to changes in money supply.
(iii) Policy Formulation: Results from correlation analysis can guide policymakers. For example, understanding factors correlated with price rises helps the government design measures to control inflation.
Q.8. What is scatter diagram?
Ans: A scatter diagram is a graphical method that plots paired observations (X, Y) on a two-dimensional graph. It visually shows the direction and approximate strength of the relationship between the two variables by the pattern formed by the points.
Q.9. What is the line of best fit?
Ans: The line of best fit is a straight line drawn through the cloud of points in a scatter diagram so that it represents the general trend of the data. It summarises the relationship and helps to make simple predictions about one variable from the other.
Q.10. State one shortcoming of scatter diagram.
Ans: A scatter diagram does not provide a precise numerical measure of the degree of correlation. It only gives a visual impression of direction and strength but cannot quantify the exact extent of association between variables.
Q.11. What type of correlations exists between variables if points lie very close to the line of best fit in an upward direction?
Ans: If points lie very close to the line of best fit in an upward direction, there exists a high positive linear correlation between the variables - meaning they move together strongly in the same direction.
Q.12. State the merits of scatter diagram.
Ans: The merits of scatter diagram are:
(i) It is a very simple and easy method for studying the relationship between two variables.
(ii) It visually indicates the nature of the relationship at a glance - whether positive, negative or none.
(iii) This method is not greatly affected by a few extreme values; the overall pattern remains visible.
Q.13. What are the demerits of scatter diagram?
Ans: The demerits of scatter diagram are:
(i) A scatter diagram does not measure the precise extent (numerical degree) of correlation.
(ii) It is not a quantitative method for measuring the relationship between variables.
(iii) The relationship among more than two variables cannot be shown clearly using a simple two-variable scatter diagram.
Q.14. Define Karl Pearson's coefficient of correlation.
Ans: Karl Pearson's coefficient of correlation is a numerical measure (usually denoted by r) that gives the degree and direction of linear relationship between two variables. Its value ranges between -1 and +1, where values near +1 indicate strong positive linear correlation and values near -1 indicate strong negative linear correlation.
Q.15. State any one property of correlation coefficient.
Ans: Correlation coefficient (r) is a unit-free (dimensionless) number; it has no unit because it is derived from standardized quantities and represents only the strength and direction of association between variables.
