APPSC Paper I · Assistant Statistical Officer Paper II · Topic 9
9 APPSC Paper I Correlation questions with answers
26 questions from APPSC ASO 2025 Paper II question paper with answers and APPSC ASO Paper II Mock 1 with answers. Try each one, then tap Show answer.
Previous-paper questions are as in the original paper. Medha AI wrote the answers and explanations.
9.1Karl Pearson's & Spearman's correlation, probable errorNotes
-
Consider the following information in two lists A and B:
LIST A LIST B (i) Correlation between Income and expenditure of a family (i) Positive correlation (ii) Correlation between age and weight among newly born babies (ii) Negative correlation (iii) Correlation between age and weight among very old persons (iii) High positive correlation Show answerHide answer
Answer A. A(i)-B(i), A(ii)-B(iii), A(iii)-B(ii)
Family expenditure rises with income (positive), babies gain weight steadily with age (high positive), and very old people tend to lose weight with age (negative).
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q73, final key
-
Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Karl Pearson' correlation coefficient between two variables X and Y is - 1.
Reason (R): The two variables are perfectly positively correlated.
In the context of the above two statements, which of the following is correct?
Show answerHide answer
Answer C. Assertion (A) is correct but Reason (R) is wrong.
Taking A as given (r = −1, a possible value), it cannot be explained by perfect positive correlation: r = −1 means perfect negative correlation. So A stands and R is wrong.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q80, final key
-
Karl Pearson's coefficient of correlation cannot exceed ________.
Show answerHide answer
Answer A. 1
Pearson's r always lies between −1 and +1, so it can never exceed 1.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q81, final key
-
Correlation is used to find ______ of a linear relationship between two variables.
Show answerHide answer
Answer C. strength and direction
The sign of the correlation coefficient gives the direction (positive or negative) and its absolute size gives the strength of the linear relationship.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q82, final key
-
Correlation between the age and weight of old persons above 70 years of age is expected to be:
Show answerHide answer
Answer B. negative
In old age, weight tends to fall as age rises, so the two move in opposite directions: negative correlation.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q83, final key
-
Which of the following statements is/are correct?
Statement I: If two variables X and Y are independent then rXY = 0.
Statement II: If rXY = 0, then two variables X and Y are independent.
Show answerHide answer
Answer A. Only Statement I is correct
Independence implies zero covariance and hence r = 0, but r = 0 only rules out a linear relationship; the variables may still be related non-linearly (e.g. Y = X^2), so the converse fails.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q108, final key
-
The rank correlation coefficient between two characteristics of 4 students was worked out to be 0.5. Later on it was noticed that the difference in ranks in the two characteristics obtained by one of the students was wrongly taken as 1 instead of 2. The corrected rank correlation is:
Show answerHide answer
Answer A. 1/5
0.5 = 1 - 6*Sum d^2/(4*15) gives Sum d^2 = 5. Correcting d from 1 to 2 adds 4 - 1 = 3, so Sum d^2 = 8 and rho = 1 - 48/60 = 0.2 = 1/5.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q109, final key
-
If correlation coefficient between X and Y based on 16 pairs of observations is 0.80, then probable error is:
Show answerHide answer
Answer B. 0.06
P.E. = 0.6745 (1 - r^2)/sqrt(n) = 0.6745 x 0.36/4 = 0.0607, about 0.06.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q110, final key
-
If COV(X,Y) = -16.5, Var(X) = 2.89 and var(Y) = 100, then rXY is:
Show answerHide answer
Answer C. -0.97
r = Cov/(SDx x SDy) = -16.5/(1.7 x 10) = -0.97.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q111, final key
-
On the basis of the following statements,
1. If the ranks in the first series are completely reversed in the second series, then Spearman's Rank Correlation coefficient s equal to -1.
2. Spearman's Rank Correlation coefficient is computed only for quantitative variables.
3. When only two individuals are ranked by two judges, then Spearman's Rank Correlation coefficient takes only -1 and 1 values.
Which of the following is true?
Show answerHide answer
Answer B. 1 and 3 are true
Completely reversed ranks give rho = -1; with n = 2, Sum d^2 is 0 or 2 so rho = 1 - Sum d^2 is 1 or -1. Rank correlation is designed for qualitative (rankable) attributes, so statement 2 is false.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q117, final key
-
Consider the following information in two lists A and B:
List A List B (i) Scatter Diagram (i) Can not be used for finding correlation in a grouped frequency distribution. (ii) Matrix Plot (ii) Provides measure of correlation between two variables without ranking (iii) Karl Pearson Coefficient of correlation (iii) Provides rough measure of correlation between two variables (iv) Spearman's Rank Correlation (iv) Provides rough measure of correlation among several variables Match the List – A with List – B and select the correct option.
Show answerHide answer
Answer C. A(i)-B(iii), A(ii)-B(iv), A(iii)-B(ii), A(iv)-B(i)
A scatter diagram gives a rough visual idea of correlation between two variables; a matrix plot does the same for several variables at once; Karl Pearson's r measures correlation from actual values (no ranking); Spearman's rank method cannot be applied to a grouped frequency distribution.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q124, final key
-
If X ~ N(0,1) and Y = X^2 then rXY is:
Show answerHide answer
Answer D. 0
Cov(X, X^2) = E(X^3) - E(X)E(X^2) = 0 - 0 = 0 because odd moments of N(0,1) vanish, so r = 0 even though Y is a function of X.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q133, final key
-
Given that X, Y and Z = (X + 2Y) are variables such that Var(X) = 4, Var(Y) = 3 and Var(Z) = 4, then rXY is:
Show answerHide answer
Answer C. -sqrt(3)/2
Var(Z) = Var(X) + 4Var(Y) + 4Cov(X,Y) gives 4 = 4 + 12 + 4Cov, so Cov = -3 and r = -3/(2 x sqrt(3)) = -sqrt(3)/2.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q135, final key
-
While ranking a series, three items tie for the 4th place. What rank is given to each of them?
Show answerHide answer
Answer D. 5
The three items occupy ranks 4, 5 and 6, so each gets their mean, (4 + 5 + 6)/3 = 5. The next item gets rank 7.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
If r = 0.9 for 25 pairs of observations, what is the probable error of r?
Show answerHide answer
Answer B. 0.0256
PE = 0.6745 (1 − r²)/√n = 0.6745 × (1 − 0.81)/√25 = 0.6745 × 0.19/5 = 0.0256.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
Assertion (A): If the ranks of n items in one series are exactly the reverse of the ranks in the other, Spearman's rank correlation coefficient is −1.
Reason (R): Spearman's rank correlation coefficient can be applied only to quantitative data.
Show answerHide answer
Answer C. (A) is true but (R) is false
Completely reversed ranks give Σd² = n(n² − 1)/3 and R = 1 − 2 = −1, so A is true. Rank correlation is meant precisely for qualities such as beauty or honesty that can be ranked but not measured, so R is false.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
Consider the following statements about interpreting r with its probable error (PE):
1. If r is less than PE, the correlation is not significant.
2. If r is more than six times PE, the correlation is definitely significant.
3. r ± PE gives the limits within which the population correlation coefficient may be expected to lie.
Which of the statements given above are correct?
Show answerHide answer
Answer D. 1, 2 and 3
All three are the standard rules: r < PE means no evidence of correlation; r > 6 PE means correlation is certain; ρ = r ± PE gives the limits.
Source: S.P. Gupta, Statistical Methods, Correlation Analysis
-
The coefficient of correlation between heights in centimetres and weights in kilograms of a group is 0.72. If heights are converted to inches (1 inch = 2.54 cm) and weights to pounds (1 kg = 2.2 lb), the new coefficient is
Show answerHide answer
Answer B. 0.72
Converting units multiplies each variable by a positive constant. r is independent of change of scale, so it remains 0.72.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
Which of the following statements about the probable error (PE) of r are correct?
1. PE = 0.6745 × standard error of r.
2. r ± PE gives the limits within which the population coefficient of correlation is expected to lie.
3. PE is a reliable guide even for very small samples such as n = 5.
Select the correct answer:
Show answerHide answer
Answer A. 1 and 2 only
PE = 0.6745 (1 − r²)/√n = 0.6745 × SE, and r ± PE are the usual limits for ρ. The rule assumes a fairly large sample from a normal population, so it misleads for tiny samples.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
Find Spearman's rank correlation coefficient, with the correction for tied ranks (to three decimals), for:
X: 25, 30, 30, 42, 18, 35, 30
Y: 60, 54, 58, 70, 45, 58, 50
Show answerHide answer
Answer C. 0.536
Ranks X: 6, 4, 4, 1, 7, 2, 4; Y: 2, 5, 3.5, 1, 7, 3.5, 6. Σd² = 23.5. Correction: X has 30 three times, 3(3² − 1)/12 = 2; Y has 58 twice, 2(2² − 1)/12 = 0.5. R = 1 − 6(23.5 + 2.5)/(7 × 48) = 0.536.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
Consider the following statements about correlation:
1. A high value of r proves that changes in X cause changes in Y.
2. Correlation between two variables may arise because both are influenced by a third variable.
Which of the statements given above is/are correct?
Show answerHide answer
Answer B. 2 only
Correlation measures association, not causation. Two variables may be correlated because both depend on a common third factor (e.g. sales of ice cream and cold drinks both depend on temperature).
Source: S.P. Gupta, Statistical Methods, Correlation Analysis
-
For 7 pairs of ranks, the sum of squares of the rank differences is 14. What is Spearman's rank correlation coefficient?
Show answerHide answer
Answer A. 0.75
R = 1 − 6Σd²/[n(n² − 1)] = 1 − (6 × 14)/(7 × 48) = 1 − 84/336 = 0.75.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
Which of the following are limitations of Karl Pearson's coefficient of correlation?
1. It is strongly affected by extreme values.
2. It assumes a linear relationship between the variables.
3. It cannot be computed when the two variables are in different units.
4. A high value does not by itself show cause and effect.
Select the correct answer:
Show answerHide answer
Answer B. 1, 2 and 4 only
r is sensitive to extreme items, measures only linear association and cannot show causation. It is a pure number, so X and Y may be in any units.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
Marks of 8 candidates in two papers are:
Paper I: 60, 54, 54, 60, 50, 83, 54, 44
Paper II: 55, 44, 38, 47, 36, 47, 54, 44
What is Spearman's rank correlation coefficient after correcting for tied ranks (to three decimals)?
Show answerHide answer
Answer B. 0.601
Ranks I: 2.5, 5, 5, 2.5, 7, 1, 5, 8; II: 1, 5.5, 7, 3.5, 8, 3.5, 2, 5.5. Σd² = 30. Ties: 60 twice (0.5), 54 three times (2), 47 twice (0.5), 44 twice (0.5); total 3.5. R = 1 − 6 × 33.5/(8 × 63) = 0.601.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
A district planner has only the ranks of 13 districts on literacy and on infant mortality, not the actual figures. Which measure should be used to study their relationship?
Show answerHide answer
Answer D. Spearman's rank correlation coefficient
When only ranks are known (ordinal data), Spearman's rank correlation R = 1 − 6Σd²/[n(n² − 1)] is the right measure.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
-
In the formula PE = 0.6745 (1 − r²)/√n for the probable error of r, the constant 0.6745 is used because
Show answerHide answer
Answer D. in a normal distribution, 50% of the values lie within ±0.6745 standard errors of the mean
PE = 0.6745 × SE of r. In a normal distribution the middle 50% lies within mean ± 0.6745 SE, so the population coefficient lies within r ± PE with an even (50 : 50) chance.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
Practise more Correlation. The app has more questions on this topic, picks new ones first and brings back the ones you got wrong.
All APPSC Paper I topics · APPSC Paper I syllabus · Start free
Medha AI is an independent preparation service. It is not affiliated with, endorsed by or connected to APPSC, TSPSC, MPSC, UPSC or any other commission or government body.