SUMMARY: The chapter on Correlation in Class 11 Economics focuses on understanding the statistical measure that describes the degree to which two variables move in relation to each other.
KEY TOPICS: correlation coefficient, positive correlation, negative correlation, zero correlation, scatter diagram, Karl Pearson's method, Spearman's rank correlation, properties of correlation, interpretation of correlation, limitations of correlation
The value of Karl Pearson's correlation coefficient always lies between:
A correlation coefficient of −1 indicates:
Spearman's rank correlation is most useful when:
In a scatter diagram all points lying on a straight upward-sloping line indicate:
Correlation does NOT imply:
Which of the following values of correlation coefficient indicates a perfect positive correlation?
When two variables move in opposite directions, the correlation between them is called:
A scatter diagram in which all points lie on a straight line sloping downward from left to right indicates:
Karl Pearson's coefficient of correlation is also known as:
If the correlation coefficient between two variables X and Y is +0.8, what does this indicate?
Spearman's rank correlation coefficient is most appropriately used when:
The formula for Spearman's rank correlation coefficient is r = 1 - [6ΣD²/n(n²-1)]. What does 'D' represent in this formula?
Which of the following is a limitation of using correlation analysis?
If ΣD² = 0 in Spearman's rank correlation formula, the value of the rank correlation coefficient will be:
For two variables X and Y, if the deviations from their respective means are dx and dy, Karl Pearson's correlation coefficient r is given by which of the following expressions?
Define correlation and distinguish between positive and negative correlation.
State the range within which Karl Pearson's correlation coefficient lies.
What is a scatter diagram and what does it show?
What is Spearman's rank correlation?
Why does 'correlation not imply causation'?
Define correlation and state its significance in statistical analysis.
What is a scatter diagram? How is it useful in studying correlation?
Distinguish between positive correlation and negative correlation with one example each.
What is zero correlation? Give an example.
State any two important properties of the correlation coefficient.
Explain different methods of studying correlation.
Compute Karl Pearson's coefficient of correlation for the following data: X = 2, 4, 6, 8, 10; Y = 3, 7, 5, 13, 12.
Distinguish between correlation and causation with an economic example.
Compute Spearman's rank correlation coefficient for the following marks of 5 students in two subjects: Eco: 85, 70, 60, 52, 90; Stats: 88, 65, 70, 55, 92.
Explain the types of correlation based on the direction and shape of the relationship.
Compare positive and negative correlation with the help of a table giving examples.
Assertion (A): Karl Pearson's correlation coefficient lies between −1 and +1.
Reason (R): It is a normalised measure of the linear association between two quantitative variables.
Assertion (A): A high correlation between two variables does not prove that one causes the other.
Reason (R): A common third factor, or coincidence, can produce correlation without any underlying causal link.
Assertion (A): Spearman's rank correlation is suitable for qualitative data.
Reason (R): It uses ranks instead of actual values, which makes it applicable when data can be ordered but not precisely measured.
Assertion (A): A scatter diagram indicates the direction of correlation.
Reason (R): Points trending upward from left to right suggest positive correlation, while downward points suggest negative correlation.
Assertion (A): Zero correlation means the two variables are completely unrelated.
Reason (R): Karl Pearson's coefficient is zero when there is no linear association between the two variables.
Assertion (A): Correlation coefficient always lies between -1 and +1.
Reason (R): The correlation coefficient measures the strength and direction of the linear relationship between two variables and is bounded by these limits.
Assertion (A): A scatter diagram where all points lie on a straight line sloping downward indicates perfect negative correlation.
Reason (R): When all plotted points fall exactly on a downward sloping straight line, the correlation coefficient equals -1.
Assertion (A): Karl Pearson's coefficient of correlation is also known as the product moment correlation coefficient.
Reason (R): Spearman's rank correlation is based on the ranks of observations rather than their actual values.
Statement 1: Correlation measures the degree of association between two variables.
Statement 2: Regression quantifies how one variable is predicted from another.
Statement 1: Karl Pearson's coefficient assumes a linear relationship between variables.
Statement 2: It can be influenced by extreme values in the data.
Statement 1: Rank correlation was developed by Spearman.
Statement 2: Product-moment correlation was developed by Karl Pearson.
Statement 1: Correlation can be positive or negative.
Statement 2: The sign of the correlation coefficient shows the direction of the association.
Statement 1: A scatter diagram is a graphical method for assessing correlation.
Statement 2: It provides a visual idea of the direction and the approximate strength of the association.
Statement 1: Correlation coefficient measures the degree and direction of linear relationship between two variables.
Statement 2: A correlation coefficient value of +1 indicates a perfect positive correlation between two variables.
Statement 1: In a scatter diagram, when points are scattered randomly without any pattern, it indicates zero correlation.
Statement 2: A scatter diagram can only show positive correlation between two variables.
Statement 1: Negative correlation means that as one variable increases, the other variable also increases.
Statement 2: The relationship between price and demand is a classic example of negative correlation.
Study the paired data and answer:
| X | Y |
|---|---|
| 2 | 3 |
| 4 | 7 |
| 6 | 5 |
| 8 | 13 |
| 10 | 12 |
Study the correlation interpretation guide and answer:
| r range | Interpretation |
|---|---|
| 0.9 - 1.0 | Very strong positive |
| 0.7 - 0.9 | Strong positive |
| 0.4 - 0.7 | Moderate positive |
| 0.0 - 0.4 | Weak |
| Negative | Same magnitudes with opposite sign |
Calculate Karl Pearson's correlation coefficient between price (X) and quantity demanded (Y).
| Price (₹) | Quantity demanded |
|---|---|
| 10 | 50 |
| 20 | 45 |
| 30 | 35 |
| 40 | 25 |
| 50 | 15 |
Compute Spearman's rank correlation coefficient between the two judges' rankings.
| Contestant | Judge A rank | Judge B rank |
|---|---|---|
| P | 1 | 2 |
| Q | 2 | 1 |
| R | 3 | 3 |
| S | 4 | 5 |
| T | 5 | 4 |
Study the scatter diagram of income and consumption and answer:
Based on the given scatter diagram, answer the following:
Based on the given scatter diagram showing the relationship between advertising expenditure and sales revenue of a company, answer the following:
Based on the given diagram showing the classification of types of correlation, answer the following:
Pick the question mix, set the marks, hit generate. You get a ready-to-print paper with an answer key.
Generate your paper — free