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CBSE · Class 11 · Social Science

Correlation

Standard difficulty · 20 questions · 40 marks · Time: 38 minutes

Name: Date: Score: ____ / 40

Write full answers in Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
When two variables move in the same direction, the correlation is:
  1. zero
  2. undefined
  3. negative
  4. positive
2.
Which pair of variables has positive correlation?
  1. height and weight of children
  2. a student’s roll number and height
  3. the day of the month a person was born and their weight
  4. shoe size and marks in economics
3.
What does r = −1 show?
  1. low positive correlation
  2. low negative correlation
  3. perfect positive correlation
  4. perfect negative correlation
4.
For 8 pairs of ranks, Σd2 = 92. Find Spearman’s rank correlation coefficient.
  1. −0.10
  2. −7.76
  3. 1.10
  4. 0.00
5.
Which of these can NOT be a value of the correlation coefficient r?
  1. 0.8
  2. 0.35
  3. −3
  4. −1
6.
The covariance of X and Y is −27, the standard deviation of X is 6 and of Y is 9. Find r.
  1. −1
  2. 0.5
  3. −0.5
  4. −1.8
7.
Ranks of 6 students in two subjects: Economics 1, 2, 3, 4, 5, 6; Maths 5, 3, 2, 1, 6, 4. Find Σd2.
  1. 64
  2. 34
  3. 12
  4. 32
8.
From deviations about the means, Σxy = 97, Σx2 = 144 and Σy2 = 256. Find Karl Pearson’s coefficient of correlation.
  1. −0.51
  2. 0.51
  3. 0.24
  4. 0.67
Section B — Short answer8 × 2 = 16 marks
9.
What is correlation?
10.
Two judges rank 6 contestants. Judge A: 1, 2, 3, 4, 5, 6. Judge B: 4, 6, 3, 5, 1, 2. Find Spearman’s rank correlation coefficient.
11.
Find Karl Pearson’s coefficient of correlation for X: 17, 6, 17, 9, 6 and Y: 94, 61, 95, 67, 63 (to two decimal places).
12.
Is the correlation positive, negative, or is there no correlation? (a) the speed of a car and the time to cover a fixed distance (b) the number of letters in a name and monthly income
13.
Explain each term: (a) spurious correlation (b) linear relationship
14.
The covariance of two variables is 66, and their standard deviations are 12 and 10. Find r and say what kind of correlation it shows.
15.
Marks of five students in Economics: 91, 96, 65, 67, 52; in Statistics: 58, 93, 57, 40, 42. Rank each (highest = 1), then find Spearman’s rank correlation.
16.
Given Σxy = 23, Σx2 = 162 and Σy2 = 162 (deviations from the means), find r and describe the correlation.
Section C — Longer answers4 × 4 = 16 marks
17.
Explain the scatter diagram with different patterns.
18.
For X: 8, 10, 17, 16, 19 and Y: 50, 54, 53, 56, 62: (a) find the means of X and Y (b) find Σxy, Σx2 and Σy2 using deviations from the means (c) find r to two decimal places (d) describe the correlation.
19.
Two judges rank 7 entries in a contest. Judge A: 1, 2, 3, 4, 5, 6, 7. Judge B: 5, 6, 2, 3, 4, 1, 7. (a) Find each d and Σd2. (b) Find Spearman’s coefficient. (c) Do the judges broadly agree?
20.
Say what kind of correlation you expect, and draw a rough scatter diagram for each: (a) the speed of a car and the time to cover a fixed distance (b) a student’s roll number and height. Why does a high r not prove that one causes the other?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Social Science

Answer key

Correlation · AW-11SS-ECR-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) positive—
2(a) height and weight of children—
3(d) perfect negative correlation—
4(a) −0.10rs = 1 − 6 × 92 ÷ (83 − 8) = 1 − 552 ÷ 504
5(c) −3—
6(c) −0.5r = −27 ÷ (6 × 9)
7(d) 32d = −4, −1, 1, 3, −1, 2
8(b) 0.51r = 97 ÷ √(144 × 256) = 97 ÷ 192
9A measure of the direction and intensity of the linear relationship between two variables.—
10−0.66Σd2 = 58; rs = 1 − 6 × 58 ÷ (63 − 6) = 1 − 348 ÷ 210
110.99Σxy = 380, Σx2 = 126, Σy2 = 1160; r = Σxy ÷ √(Σx2 × Σy2)
12(a) negative (b) no correlation—
13(a) a chance correlation between unrelated variables (b) a relationship shown by a straight line—
14r = 0.55; positive correlation66 ÷ (12 × 10)
15ranks 2, 1, 4, 3, 5 and 2, 1, 3, 5, 4; rs = 0.7Σd2 = 6; 1 − 6 × 6 ÷ 120
16r = 0.14; positive correlation√(162 × 162) = 162
17Points rising from left to right show positive correlation, falling show negative, a straight line shows perfect correlation, and a shapeless spread shows no correlation.—
18(a) 14, 55 (b) 65, 90, 80 (c) 0.77 (d) positive, highr = Σxy ÷ √(Σx2 × Σy2)
19(a) d = −4, −4, 1, 1, 1, 5, 0; Σd2 = 60 (b) −0.07 (c) no, their rankings move in opposite directionsrs = 1 − 6 × 60 ÷ (73 − 7) = 1 − 360 ÷ 336
20(a) negative (b) no correlation; the link may be by chance or due to a third factor.—