Important Questions and Answers for Class 11 Economics Chapter 6 Correlation 2025-26

1. Multiple choice questions.

Q1. Which of the following best describes correlation?

• (a) It shows cause and effect relationship between two variables
• (b) It measures the degree of association between two variables
• (c) It analyses data graphically only
• (d) It means variables are unrelated

Answer: (b) It measures the degree of association between two variables. Correlation helps to study the strength and direction of the relationship.

Q2. The value of Pearson’s correlation coefficient (r) lies between:

• (a) 0 and 1
• (b) -1 and +1
• (c) -infinity and +infinity
• (d) 1 and 100

Answer: (b) -1 and +1. 'r' always ranges from -1 to +1 in simple correlation.

Q3. When two variables move in the same direction, the correlation is:

• (a) Negative
• (b) Zero
• (c) Positive
• (d) None

Answer: (c) Positive. Positive correlation means both variables increase or decrease together.

Q4. The correlation coefficient has:

• (a) The same unit as variables measured
• (b) No unit
• (c) Percentage
• (d) km/hr

Answer: (b) No unit. Correlation coefficient is a pure number, without any units.

Q5. Which technique is best for visualising the association between two variables before calculation?

• (a) Scatter diagram
• (b) Covariance
• (c) Step deviation method
• (d) Rank correlation

Answer: (a) Scatter diagram. It gives a visual idea of relationship before numerical calculation.

2. Very Short Answer (VSA).

Q6. Define correlation in statistics.

Answer: Correlation is the statistical measure that describes the direction and degree of relationship between two variables, showing how they move together.

Q7. What is meant by positive correlation?

Answer: Positive correlation means that both variables move in the same direction; as one increases, the other also increases.

Q8. Name two methods for measuring correlation quantitatively.

Answer: Two quantitative methods are (i) Karl Pearson’s correlation coefficient and (ii) Spearman’s rank correlation.

Q9. What does a correlation coefficient of zero indicate?

Answer: A coefficient of zero means there is no linear relationship between the two variables under study.

Q10. Write one feature of the correlation coefficient.

Answer: The correlation coefficient is a pure number; it does not have any unit of measurement.

3. Short Answer Questions.

Q11. Distinguish between positive and negative correlation with suitable examples.

Answer: Positive correlation exists when variables move in the same direction, like income and consumption. Negative correlation is when variables move oppositely, such as price and quantity demanded. For example, as income rises, people usually spend more (positive), but as apple prices rise, demand may fall (negative).

Q12. Explain the scatter diagram method for studying correlation.

Answer: In a scatter diagram, pairs of values for two variables are plotted as points on a graph. The pattern shows direction and strength of the relationship: points close to a rising line suggest positive correlation, while random scatter indicates no correlation.

Q13. List two properties of Karl Pearson’s correlation coefficient.

Answer: First, the coefficient $r$ always lies between $-1$ and $+1$. Second, $r$ has no units and is unaffected by change of origin and scale.

Q14. When is Spearman’s rank correlation preferred over Pearson’s correlation?

Answer: When precise numerical values are unavailable or data is qualitative (like beauty or fairness), or the relationship is monotonic but not linear, Spearman’s rank correlation is best used instead of the Pearson coefficient.

4. Long Answer Questions.

Q15. Describe the meaning, characteristics, and types of correlation, giving at least two examples for each.

Answer: Correlation means systematic co-variation between two variables. Its main features are: it does not reveal cause and effect; it only measures the degree and direction of association, not units. There are two types: Positive (height and weight, income and consumption) where variables move together, and Negative (price and demand, rainfall and need for irrigation) where variables move oppositely.

1. Define correlation as the co-variation between two variables.
2. State characteristics: no causal link, bounded between -1 and +1, no units.
3. Explain positive correlation with examples: height and weight, income and spending.
4. Describe negative correlation, such as price and demand, study time and chances of failure.

Q16. Explain Karl Pearson’s correlation coefficient method. Write formulae and discuss the steps for computation.

Answer: Karl Pearson’s coefficient gives a precise value for degree of linear relationship between two variables. It uses mean and standard deviation. Its formula is: $r = \dfrac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y}$. The calculation involves computing means, deviations, covariance, and dividing by the product of their standard deviations.

1. Find the means of $X$ and $Y$.
2. Calculate deviations $(X - \bar X)$ and $(Y - \bar Y)$.
3. Compute covariance as $\sum (X - \bar X)(Y - \bar Y) / N$.
4. Find standard deviations of $X$ and $Y$.
5. Divide covariance by product of standard deviations to get $r$.

5. Assertion–Reason type questions.

Assertion (A): Correlation coefficient can never be greater than +1 or less than -1.
Reason (R): Any value above +1 or below -1 indicates a calculation mistake.

• (a) A and R are true, and R is the correct explanation of A
• (b) A and R are true, but R is not the correct explanation of A
• (c) A is true, but R is false
• (d) A is false, but R is true

Answer: (a) A and R are true, and R explains A. Correlation coefficient is always between -1 and +1.

Assertion (A): Correlation measures co-variation, not causation.
Reason (R): Presence of correlation does not mean that one variable causes changes in the other.

• (a) A and R are true, and R is the correct explanation of A
• (b) A and R are true, but R is not the correct explanation of A
• (c) A is true, but R is false
• (d) A is false, but R is true

Answer: (a) A and R are true, and R correctly explains A. Correlation does not imply a causal relationship.

6. Case-based questions.

A group of students tracked the daily temperature and ice-cream sales in their city for a week. They noticed as temperature increased, sales also rose. They plotted pairs (temperature, sales) as dots on a scatter diagram, which mostly lined up in an upward trend.

(i) What type of correlation is shown between temperature and ice-cream sales?

Answer: Positive correlation, as both variables increase together.

(ii) Name the graphical tool the students used to visualise this association.

Answer: Scatter diagram.

(iii) If the dots were widely scattered with no pattern, what would this indicate?

Answer: It would indicate no correlation between temperature and sales.

(iv) What is the correlation coefficient value expected in perfect positive correlation?

Answer: The value would be +1 in perfect positive correlation.

7. Numericals / Derivations.

Q7. Calculate the correlation coefficient (r) for the following data:
X: 1, 3, 4, 5, 7, 8
Y: 2, 6, 8, 10, 14, 16

Answer: $r = 1$. Steps:

1. Given X and Y values: 6 pairs
2. $r = \dfrac{N\sum XY - (\sum X)(\sum Y)}{\sqrt{[N \sum X^2 - (\sum X)^2][N\sum Y^2 - (\sum Y)^2]}}$
3. Upon calculation, $r = 1$
4. There is perfect positive linear correlation

Q8. Spearman’s rank correlation: Two students obtain the following marks in two subjects.
Student: A, B, C, D, E
X (Stats): 85, 60, 55, 65, 75
Y (Eco): 60, 48, 49, 50, 55
Calculate the rank correlation coefficient.

Answer: Assign ranks, find differences, and use formula:

1. Rank X: 1 (A), 2 (E), 3 (D), 4 (B), 5 (C)
2. Rank Y: 1 (A), 2 (E), 3 (D), 4 (C), 5 (B)
3. D: 0, 0, 0, 0, -1; $D^2$ sum = 2
4. $r_s = 1 - \frac{6 \sum D^2}{n(n^2-1)} = 1 - \frac{12}{120} = 0.9$
5. Strong positive rank correlation

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