APPSC Paper I · Assistant Statistical Officer Paper II · Topic 6
6 APPSC Paper I Statistics: Data, Sampling & Presentation questions with answers
32 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.
6.1Frequency distribution, tabulation & diagramsNotes
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On the basis of the following statements,
1. Frequency distribution is a tabular arrangement of data in form of classes
2. Open class interval does not have upper or lower limit
3. For summarizing large mass of raw data, it is useful to distribute data into classes
Which of the following holds?
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Answer D. All three are true
A frequency distribution tabulates data by classes, an open-end class lacks either a lower or an upper limit, and grouping into classes is the standard way to summarise large raw data, so all three statements are true.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q71, final key
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The most appropriate diagram for representing the distribution of National plan outlay of a country in different sectors of economy is:
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Answer D. Pie Chart
A pie chart shows how a total (the plan outlay) is divided among parts (sectors), each sector's share drawn as an angle of the circle.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q77, final key
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Match the List – I with List – II and select the correct answer from the options given below:
List-I List-II A-Bar Diagram (i) A graphical representation of grouped frequency distribution with continuous classes. B- Histogram (ii) Diagram consists of a number of rectangles used for one dimensional comparison C-Line Graph (iii) A graphical representation technique that displays data in a circular-shaped graph D-Pi-chart (iv) A graph that utilizes points and lines to represent change over time Show answerHide answer
Answer C. A-ii, B-i, C-iv, D-iii
Bar diagrams are one-dimensional rectangles (A-ii), a histogram shows a grouped continuous frequency distribution (B-i), a line graph joins points to show change over time (C-iv), and a pie chart is circular (D-iii).
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q86, final key
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Given below are two statements labelled as Assertion (A) and Reasoning (R).
Assertion (A): Class mark is obtained by dividing the sum of lower and upper class limits, by two
Reasoning (R):. Class boundaries are used for making the class intervals continuous
In light of the above statements, choose the correct option.
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Answer B. Both A and R are true and R is not correct explanation of A.
The class mark (mid-value) is (lower limit + upper limit)/2, and class boundaries are used to make inclusive classes continuous. Both are true, but the second does not explain the first.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q90, final key
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Match the following:
Column I Column II 1. Multiple bar diagrams I. drawn by joining the mid-points of all tops of a histogram 2. Pie Diagram II. drawn to represent the time series data related to the temperature, rainfall, population growth, 3. Line Diagram III. drawn to depict the total value of the given attribute using a circle. 4. Frequency polygon IV. constructed to represent two or more than two variables for the purpose of comparison Choose the correct option.
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Answer B. 1-IV; 2-III; 3- II; 4-I
Multiple bars compare two or more variables (1-IV), a pie diagram shows a total using a circle (2-III), a line diagram shows time series such as rainfall or population (3-II), and a frequency polygon joins the mid-points of histogram tops (4-I).
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q98, final key
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The heights of rectangles in a histogram with class intervals of equal sizes are proportional to:
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Answer A. Class frequencies
In a histogram the area of each rectangle is proportional to the class frequency; when all widths are equal, the heights are therefore proportional to the class frequencies.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q105, final key
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Which of the following is NOT true about a frequency polygon?
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Answer C. It can't be constructed for unequal class intervals.
A frequency polygon can be drawn for unequal class intervals too, after adjusting frequencies (frequency densities); the other statements describe how it is drawn and closed.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q120, final key
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The class marks of a continuous frequency distribution with equal classes are 15, 25, 35 and 45. What are the limits of the class whose class mark is 35?
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Answer C. 30 – 40
Class width = difference between consecutive class marks = 10. Lower limit = 35 − 10/2 = 30 and upper limit = 35 + 10/2 = 40.
Source: Standard method; answer and every option computed and checked in Python
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A frequency distribution uses the inclusive classes 10–19, 20–29, 30–39. What are the true class limits (class boundaries) of the class 20–29?
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Answer B. 19.5 – 29.5
Gap between the upper limit of one class and the lower limit of the next is 1, so the correction factor is 0.5. Class 20–29 becomes 19.5–29.5.
Source: Standard method; answer and every option computed and checked in Python
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The class 40–60 of a frequency distribution has frequency 50. What is its frequency density?
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Answer A. 2.5
Frequency density = frequency ÷ class width = 50 ÷ 20 = 2.5.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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A histogram is drawn for the classes 0–10 (f = 8), 10–20 (f = 14), 20–40 (f = 30) and 40–50 (f = 6). Taking the class width 10 as standard, what should be the height (adjusted frequency) of the rectangle over 20–40?
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Answer D. 15
In a histogram with unequal classes the area of each rectangle is proportional to the frequency. For a class twice the standard width, height = 30 / 2 = 15.
Source: Standard method; answer and every option computed and checked in Python
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Which of the following is a continuous variable?
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Answer D. Weight of students in a class
A continuous variable can take every value in an interval (weight, height, time). Counts such as rooms, accidents or shareholders are discrete.
Source: NCERT Class 11 Statistics for Economics, Organisation and Presentation of Data
6.1Data collection, census & samplingNotes
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Which of the following is not a source of secondary data?
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Answer C. Autobiography
An autobiography is a first-hand account by the person concerned and is treated as a primary source, while biographies, newspapers and magazines report information compiled by others (secondary sources).
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q78, final key
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On the basis of the following statements:
1. Frequent field checks are taken up on the work of enumerators responsible for filling schedules
2. While using schedules, enumerators explain the aims and objects of the investigation and also remove the difficulties faced by any respondent
3. Questionnaires are filled by investigators for helping the respondents
Which of the options is correct?
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Answer B. 1 and 2 are true
Enumerators filling schedules are field-checked and they explain the purpose and help respondents, so 1 and 2 are true. A questionnaire is filled by the respondents themselves, not by investigators, so 3 is false.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q91, final key
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Which of the following is NOT the advantage of using Schedule over questionnaire?
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Answer C. It is very cost effective
The schedule method needs paid, trained enumerators to visit respondents, so it is costlier than a mailed questionnaire; cost-effectiveness is an advantage of the questionnaire, not the schedule.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q93, final key
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Which of the following is not true about census?
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Answer C. The first census was conducted non-synchronously in 1862
India's first (non-synchronous) census was taken in 1872, not 1862; the first synchronous census was in 1881.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q104, final key
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Out of the sampling techniques mentioned below, which is probability sampling method?
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Answer B. Cluster sampling
In cluster sampling, clusters are chosen at random so every unit has a known chance of selection; judgement and convenience sampling are non-probability methods.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q107, final key
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For collection of primary data through questionnaires, which of the following is NOT true?
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Answer D. Open-ended questions should be included as it is easy to analyze them.
Open-ended questions give varied free-text answers that are hard to tabulate and analyse, so they should be kept to a minimum; the other points are standard rules of questionnaire design.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q122, final key
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For collection of data through Schedules, which of the following does not hold?
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Answer D. Reliability of collected data does not depend upon capability of enumerator
In the schedule method enumerators ask the questions and record the answers themselves, so the quality of the data depends heavily on their skill and honesty.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q132, final key
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Consider the following statements:
1. Non-sampling errors can arise in both census and sample surveys.
2. Non-sampling errors are usually larger in a census than in a sample survey.
3. Sampling error can be reduced by increasing the sample size.
4. Non-response is a sampling error.
Which of the statements given above are correct?
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Answer B. 1, 2 and 3 only
Non-sampling errors (from faulty measurement, non-response, processing mistakes, bias) occur in both methods and tend to be larger in a census because of its scale and the many untrained staff. Sampling error falls with sample size. Non-response is a non-sampling error.
Source: S.P. Gupta, Statistical Methods, Sampling; Telugu Akademi B.A. Statistics
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The standard deviation of the weights of school children is 12 kg. What is the minimum simple random sample size needed to estimate the mean weight within ±2 kg with 95% confidence (z = 1.96)?
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Answer C. 139
n = (zσ/E)² = (1.96 × 12/2)² = 138.30; round up to 139, since 138 would give an error slightly above 2 kg.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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A sample of 200 households is to be selected from a list of 4,000 households by systematic sampling. The sampling fraction and the sampling interval are, respectively,
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Answer A. 5% and 20
Sampling fraction f = n/N = 200/4000 = 0.05 = 5%. Interval k = N/n = 4000/200 = 20.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Nothing is known in advance about the proportion of households using LPG in a town. What is the minimum sample size needed to estimate this proportion within ±0.03 with 95% confidence (z = 1.96)?
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Answer C. 1,068
With P unknown take P = 0.5 (largest PQ = 0.25). n = z²PQ/E² = 1.96² × 0.25/0.03² = 1067.11, rounded up to 1,068.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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A question in a household survey reads: "Does your household have a ration card? (Yes / No)". Such a question is called
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Answer C. a dichotomous question
A closed question with only two possible answers (yes/no, true/false) is a dichotomous question.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Which one of the following is NOT a probability (random) sampling method?
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Answer D. Snowball sampling
Simple random, stratified, systematic, cluster and multistage sampling give each unit a known chance of selection. Snowball sampling, where existing respondents recruit further respondents, is a non-probability method.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
6.1Probability: definitionsNotes
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Three identical dice are tossed. Probability that the same number will appear on each of them is:
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Answer B. 1/36
There are 6^3 = 216 outcomes and 6 of them show the same number on all three dice, so P = 6/216 = 1/36.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q106, final key
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For any two events A and B, P(A∪B) is equal to
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Answer B. P(A)+P(B)-P(AB)
By the addition theorem, P(A∪B) = P(A) + P(B) - P(A∩B); the overlap is subtracted once because it is counted twice.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q121, final key
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What is the probability that a leap year, selected at random, contains 53 Sundays?
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Answer B. 2/7
A leap year has 366 days = 52 weeks + 2 days. The two extra days form one of 7 equally likely pairs (Sun–Mon, Mon–Tue, …, Sat–Sun); two of them contain a Sunday, so P = 2/7.
Source: Standard method; answer and every option computed and checked in Python
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Consider the following statements about two events A and B:
1. If A and B are independent, then A and B' (complement of B) are also independent.
2. If A and B are independent, then P(A ∩ B) = P(A) + P(B).
Which of the statements given above is/are correct?
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Answer A. 1 only
P(A ∩ B') = P(A) − P(A ∩ B) = P(A) − P(A)P(B) = P(A)P(B'), so A and B' are independent. For independent events P(A ∩ B) = P(A)P(B), a product, not a sum.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
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Which of the following are axioms in the axiomatic definition of probability?
1. P(A) ≥ 0 for every event A
2. P(S) = 1, where S is the sample space
3. P(A ∪ B) = P(A) + P(B) for mutually exclusive events A and B
4. P(A ∩ B) = P(A) P(B) for any two events A and B
Select the correct answer using the code given below.
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Answer B. 1, 2 and 3 only
The axioms are non-negativity, certainty (P(S) = 1) and additivity for mutually exclusive (disjoint) events. P(A ∩ B) = P(A)P(B) holds only for independent events and is not an axiom.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
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A problem is given to three students whose chances of solving it independently are 1/2, 1/3 and 1/4. What is the probability that the problem is solved?
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Answer D. 3/4
P(no one solves) = (1/2)(2/3)(3/4) = 1/4, so P(solved by at least one) = 1 − 1/4 = 3/4.
Source: Standard method; answer and every option computed and checked in Python
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Which definition of probability is also known as 'a priori' probability?
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Answer B. Classical definition
The classical definition is called a priori because the probability is found by reasoning before the experiment is performed, assuming equally likely outcomes.
Source: Gupta and Kapoor, Fundamentals of Mathematical Statistics, Theory of Probability
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