20 multiple-choice (MCQ / objective) questions from this chapter, in the common exam-style shapes. Every question comes with an explanation along with the answer, so you remember why the option is correct, not just which one it is.
Syllabus note
CBSE 2026-27 Class 11 (Part A, Unit 3) includes this whole chapter: meaning and properties, scatter diagram, Karl Pearson’s method (two variables, ungrouped data) and Spearman’s rank correlation (non-repeated and repeated ranks). In numericals write the formula, the substitution and the answer on separate lines, then a one-line interpretation.
1 Direct Questions
Direct Questions
- 1 markCorrelation studies and measures:
(A) the cause and effect relation between variables(B) the average of one variable(C) the direction and intensity of relationship between variables(D) the collection of data - 1 markWhich of these relationships does the book call simple coincidence?
(A) Agricultural productivity and rainfall(B) Arrival of migratory birds and birth rates(C) Price and quantity demanded(D) Income and consumption - 1 markWhen income rises, consumption also rises. This is an example of:
(A) negative correlation(B) zero correlation(C) positive correlation(D) a non-linear relation - 1 markWhich measure can show any type of relationship, linear or non-linear?
(A) Karl Pearson’s coefficient of correlation(B) Spearman’s rank correlation(C) Covariance(D) Scatter diagram - 1 markThe correct statement about the range of r is:
(A) −1 ≤ r ≤ +1(B) 0 ≤ r ≤ 1(C) r can be any positive number(D) −∞ to +∞ - 1 markIf Σxy = −30, Σx² = 36 and Σy² = 100, then r =
(A) +0.5(B) −0.5(C) −0.0083(D) −0.22 - 1 markWho developed rank correlation?
(A) Karl Pearson(B) Keynes(C) British psychologist C.E. Spearman(D) R.A. Fisher - 1 markIn Example 3 (beauty contest), which two judges have the nearest approach to a common perception of beauty?
(A) A and C (rs = 0.5)(B) A and B (rs = 0.3)(C) B and C(D) All three equal - 1 markIf r between the arrival of vegetables in the mandi and their price is 0, then according to the book:
(A) price would fall very sharply(B) price would fall a little(C) supply would fall(D) there would be no fall in price even after large supplies
2 Assertion-Reason
Assertion-Reason
- 1 markAssertion (A): Ice-cream sales and deaths by drowning are highly correlated, yet ice-cream is not the cause of these deaths.
Reason (R): A third variable, temperature, affects both.
(A) Both A and R are true, and R is the correct explanation of A(B) Both 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 - 1 markAssertion (A): If r = 0, the two variables are independent.
Reason (R): r = 0 only shows that there is no linear relation between the two variables.
(A) Both A and R are true, and R is the correct explanation of A(B) Both 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 - 1 markAssertion (A): Spearman’s coefficient is not affected by extreme values.
Reason (R): Spearman’s coefficient is based on ranks instead of values.
(A) Both A and R are true, and R is the correct explanation of A(B) Both 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
3 Match the Following
Match the Following
- 1 markMatch List I with List II.
List I: (i) points on a rising line (ii) points around a falling line (iii) points scattered all over (iv) points around a rising curve
List II: (1) negative correlation (2) positive non-linear (3) perfect positive (4) no correlation
(A) i-1, ii-3, iii-4, iv-2(B) i-3, ii-4, iii-1, iv-2(C) i-3, ii-1, iii-4, iv-2(D) i-3, ii-1, iii-2, iv-4
4 Statement-Based Questions
Statement-Based Questions
- 1 markConsider these statements.
(i) r is unaffected by change of origin and scale.
(ii) The value of r lies between −1 and +1.
(A) Only (i) is true(B) Both are true(C) Only (ii) is true(D) Both are false
5 Arrange in the Correct Order
Arrange in the Correct Order
- 1 markArrange the steps for rank correlation when ranks are not given in the correct order.
1. Find D = Rx − Ry and D²
2. Rank the values of both variables
3. Put ΣD² and n into the formula
4. Check that ΣD = 0
(A) 1-2-4-3(B) 2-1-4-3(C) 2-4-1-3(D) 2-1-3-4
6 Fill in the Blanks
Fill in the Blanks
- 1 markChanging the price index to U = (X − 100)/10 is a change of ______ and of scale.
(A) origin(B) rank(C) mean(D) variance
7 Odd One Out
Odd One Out
- 1 markThree of these are techniques for measuring correlation. Which one is not?
(A) Scatter diagram(B) Karl Pearson’s coefficient(C) Arithmetic mean(D) Spearman’s rank correlation
8 Passage-Based Questions
Passage-Based Questions
Passage
(Hypothetical survey) Data for one year were collected from 8 villages of a district. Villages with more mobile towers also had higher school enrolment; r between the two was 0.82. A newspaper wrote: ‘Mobile towers send children to school.’ An economist pointed out that larger villages connected by road have both more towers and more schools.
- 1 markWhich conclusion from r = 0.82 in the passage is correct?
(A) Mobile towers increase enrolment(B) There is strong positive correlation, but it does not prove causation(C) The two variables are independent(D) The correlation is negative
Passage
Marks of 5 students in Mathematics (X) and Economics (Y): student A: 30, 20; B: 45, 35; C: 25, 30; D: 50, 45; E: 40, 25. The teacher wants to know how closely the ranks in the two subjects are related.
- 1 markGiving rank 1 to the highest marks, what are student A’s ranks (Rx, Ry)?
(A) (2, 2)(B) (5, 4)(C) (4, 4)(D) (4, 5)
9 True / False
True / False
- 1 markConsider these statements.
(i) In Example 5, the value 50 of Y appears three times.
(ii) In Example 5 there are three groups of equal values (90, 75, 50).
(iii) The total correction factor for the three groups of equal Y values is 3.
(A) (i), (ii) and (iii) are all true(B) Only (i) and (ii) are true(C) Only (iii) is true(D) Only (i) is true
Answer Key and Explanations
Direct Questions
- (c) Book: correlation studies and measures the direction and intensity of relationship among variables; it does not show causation.
- (b) The relation between the arrival of migratory birds in a sanctuary and birth rates in the locality cannot be given a cause and effect interpretation.
- (c) Both variables move in the same direction, so the correlation is positive.
- (d) The scatter diagram is not confined to linear relations; both coefficients measure linear relationship.
- (a) r always lies between −1 and +1; a value outside indicates an error in calculation.
- (b) r = −30/√(36 × 100) = −30/60 = −0.5. −0.0083 comes from forgetting the square root (−30/3600); −0.22 from adding in the denominator (136).
- (c) Book: the British psychologist C.E. Spearman.
- (a) A-B: 0.3, A-C: 0.5, B-C: −0.4 (ΣD² = 28). The highest is 0.5.
- (d) r = 0: no fall in price even after large supplies, possible if a good transport network takes the supply to other markets.
Assertion-Reason
- (a) Both A and R are true, and R explains why there is correlation without causation.
- (d) A is false: a non-linear relation can exist (for example y = x², r = 0). R is true.
- (a) Both are true; once values become ranks, even a huge value only takes the next rank, so R explains A.
Match the Following
- (c) On a line = perfect positive; around a falling line = negative; scattered = no correlation; curve = non-linear.
Statement-Based Questions
- (b) Both are properties of r.
Arrange in the Correct Order
- (b) Ranks first (2), then D and D² (1), then check ΣD = 0 (4), and finally the formula (3).
Fill in the Blanks
- (a) Subtracting 100 changes the origin, dividing by 10 changes the scale; r is unaffected by both.
Odd One Out
- (c) The arithmetic mean is a measure of central tendency, not of correlation.
Passage-Based Questions
- (b) Correlation measures covariation, not causation.
- (d) X: 50, 45, 40, 30, 25 → A (30) is rank 4; Y: 45, 35, 30, 25, 20 → A (20) is rank 5.
True / False
- (a) All three are true: the factors for m = 2, 2, 3 are 0.5 + 0.5 + 2 = 3; rs = 1 − 6(198 + 3)/1716 ≈ 0.30.
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