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.

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
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   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
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   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
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   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.
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   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.
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   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.

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