Statistics – Correlation (Scatter Diagram, Pearson’s & Spearman’s Coefficients) Quiz - ICSE Class 11 Economics

Free practice quiz: Statistics – Correlation (Scatter Diagram, Pearson’s & Spearman’s Coefficients) (ICSE Class 11 Economics). 51 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 11 Economics practice quiz has 51 multiple-choice questions on Statistics – Correlation (Scatter Diagram, Pearson’s & Spearman’s Coefficients), and 51 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. In a scatter diagram, if the points tend to cluster around a straight line sloping upwards from left to right, what type of correlation is indicated?

   1. Perfect Positive Correlation
   2. Positive Correlation
   3. Negative Correlation
   4. No Correlation
   Show answer

   Answer: B. Positive Correlation

   A straight line sloping upwards from left to right on a scatter diagram signifies that as one variable increases, the other variable also tends to increase, which is the definition of positive correlation.

2. If a scatter diagram shows points tightly clustered around a straight line sloping downwards, what is the approximate value of the Pearson's correlation coefficient?

   1. 0.9
   2. -0.9
   3. 0.1
   4. -0.1
   Show answer

   Answer: B. -0.9

   Points tightly clustered around a downward sloping line indicate a strong negative linear relationship. Pearson's correlation coefficient (r) would be close to -1. Among the given options, -0.9 represents a strong negative correlation.

3. If in a sample of 10 pairs of observations, all pairs have identical ranks for both variables, what would be the Spearman's rank correlation coefficient?

   1. 1
   2. 0
   3. -1
   4. Cannot be determined without raw data
   Show answer

   Answer: A. 1

   When all pairs of observations have identical ranks for both variables, it implies a perfect positive monotonic relationship, resulting in a Spearman's rank correlation coefficient of 1.

4. Which of the following scenarios would most likely result in a Spearman's rank correlation coefficient of 1?

   1. Ranking students by height and then by their score on a test, where taller students consistently score higher.
   2. Ranking students by their height and then by their weight, where there is no consistent trend.
   3. Ranking students by their height and then by their weight, where taller students consistently weigh less.
   4. Ranking students by their height and then by their score on a test, where taller students consistently score lower.
   Show answer

   Answer: A. Ranking students by height and then by their score on a test, where taller students consistently score higher.

   A Spearman's rank correlation coefficient of 1 indicates a perfect positive monotonic relationship between the ranks. This means that the order of students based on height is identical to the order based on test scores (if taller students consistently score higher).

5. What is the main difference between Pearson's correlation and Spearman's correlation when considering the nature of the relationship?

   1. Pearson's measures linear relationships, while Spearman's measures monotonic relationships.
   2. Pearson's measures monotonic relationships, while Spearman's measures linear relationships.
   3. Pearson's is only for positive correlations, while Spearman's is for both positive and negative.
   4. Pearson's requires ratio data, while Spearman's requires nominal data.
   Show answer

   Answer: A. Pearson's measures linear relationships, while Spearman's measures monotonic relationships.

   Pearson's product-moment correlation coefficient assesses the strength and direction of a *linear* association between two variables. Spearman's rank correlation coefficient assesses the strength and direction of a *monotonic* association, meaning it detects whether variables tend to increase or decrease together, regardless of whether the relationship is strictly linear.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If all the data points in a scatter diagram fall perfectly on a straight line sloping downwards from left to right, what is the value of the Pearson's correlation coefficient (r)?
2. Which of the following statements best describes Spearman's rank correlation coefficient?
3. If the Pearson's correlation coefficient (r) between two variables, X and Y, is 0.95, what can be inferred about their relationship?
4. A scatter diagram shows a circular cloud of points. What does this typically suggest about the correlation between the two variables?
5. Consider the following pairs of ranks for two variables A and B: (1, 2), (2, 1), (3, 3), (4, 4), (5, 5). What would be the Spearman's rank correlation coefficient?
6. If the Pearson's correlation coefficient is 0, it implies:
7. When would you choose to use Spearman's rank correlation coefficient over Pearson's correlation coefficient?
8. In a scatter diagram, if the points form a curve that goes upwards and then downwards, what is the likely value of the Pearson's correlation coefficient?
9. What is the range of possible values for both Pearson's correlation coefficient (r) and Spearman's rank correlation coefficient (ρ)?
10. Consider the data: (X: 1, 2, 3, 4) and (Y: 2, 4, 6, 8). What is the Pearson's correlation coefficient?
11. When calculating Spearman's rank correlation coefficient, what is the first step involving the raw data?
12. In a scatter plot, if the points are scattered widely with no discernible pattern, the correlation coefficient is likely to be:
13. If two variables have a Pearson's correlation coefficient of r = -0.8, what does this indicate?
14. What is the effect of an outlier on Pearson's correlation coefficient?
15. Consider the ranks of two variables X and Y: X ranks = [1, 2, 3, 4], Y ranks = [4, 3, 2, 1]. What is the Spearman's rank correlation coefficient?
16. Which graphical representation is most appropriate for visually assessing the relationship between two quantitative variables and identifying the presence and nature of correlation?
17. If the Pearson's correlation coefficient (r) is calculated to be 0.1, it suggests:
18. What is the primary assumption of Pearson's correlation coefficient regarding the data?
19. A scatter diagram shows points forming a U-shape. What would be the most appropriate conclusion about the Pearson's correlation coefficient?
20. If Pearson's r = 0.7 for variables A and B, and Pearson's r = 0.7 for variables C and D, what can we say about the strength of the linear relationship in both cases?
21. When are the Pearson's correlation coefficient and Spearman's rank correlation coefficient likely to yield similar results?
22. If a scatter diagram shows points scattered in a way that suggests a perfect quadratic relationship, what would be the value of the Pearson's correlation coefficient?
23. What does a Spearman's rank correlation coefficient of -0.2 indicate?
24. If the Pearson's correlation coefficient (r) between two variables X and Y is 0, it implies:
25. In the calculation of Spearman's rank correlation, if there are tied ranks for a variable, how are they typically handled?
26. What does it mean if a scatter diagram shows a positive correlation?
27. If the Pearson's correlation coefficient between the heights and weights of students in a class is found to be 0.85, what can be concluded?
28. If a scatter diagram shows points that form a perfect horizontal line, what is the Pearson's correlation coefficient?
29. When calculating Pearson's correlation coefficient, what is the role of the covariance between the two variables?
30. Consider the following pairs of ranks for variables P and Q: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). What is the Spearman's rank correlation coefficient?
31. If the points on a scatter diagram form a tight cluster around a straight line sloping upwards, the Pearson's correlation coefficient (r) would be:
32. What does a Pearson's correlation coefficient of -0.05 indicate?
33. Which of the following correlations would be considered the strongest negative linear relationship?
34. If the ranks of variable A are [1, 2, 3, 4, 5] and the ranks of variable B are [5, 4, 3, 2, 1], what is the Spearman's rank correlation coefficient?
35. Which type of correlation is represented by points on a scatter diagram that form a perfect curve upwards and then downwards?
36. If the Pearson's correlation coefficient between two variables is 0.5, this indicates:
37. If a scatter diagram shows points that are scattered randomly in all directions, what is the Pearson's correlation coefficient likely to be?
38. What does a Spearman's rank correlation coefficient of 0.9 indicate?
39. If the Pearson's correlation coefficient between two variables is 1, it means:
40. Which of the following is NOT a method to measure correlation?
41. If the scatter diagram shows a relationship where as X increases, Y decreases rapidly at first and then the rate of decrease slows down, what would be the Pearson's correlation coefficient?
42. When calculating Spearman's rank correlation, if the raw data are already in ranks, what is the first step?
43. Which correlation coefficient is sensitive to outliers?
44. If the scatter diagram shows points forming a perfect vertical line, what is the Pearson's correlation coefficient?
45. If the ranks of two variables are identical for all observations, what is the Spearman's rank correlation coefficient?
46. What is the coefficient of determination (r-squared) if the Pearson's correlation coefficient (r) is 0.8?

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