100+ Free BCS Written Statistics Practice Questions

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2026 Statistics

Key Facts: BCS Written Statistics Exam

200 marks

Official Statistics post-related paper (Subject Code 981)

BPSC BCS written syllabus

100 + 100

Part I and Part II marks

BPSC BCS written syllabus, Statistics

50% aggregate

Written-stage pass on the 900-mark exam (plus per-paper minima)

BPSC BCS examination page

Tk. 200 / Tk. 50

50th BCS general / reduced application fee (no separate written fee)

50th BCS circular reporting citing PSC

4 hours

Duration used here for BPSC 200-mark written papers; confirm the routine

Longstanding BPSC sitting practice

Descriptive written

Official item type (this bank is an English MCQ study adaptation)

BPSC written examination structure

BPSC Statistics (code 981) is a 200-mark, two-part descriptive written paper (100+100) inside the 900-mark BCS written stage; 50% written aggregate applies, plus per-paper minima. There is no separate written fee (50th BCS: Tk. 200 general / Tk. 50 reduced categories). This page offers English MCQs as a study aid, not an official-paper simulation.

Sample BCS Written Statistics Practice Questions

Try these sample questions to test your BCS Written Statistics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which statement best describes the definition and scope of statistics in the BCS post-related Statistics syllabus?

A.A method used only to draw pie charts of already published census tables

B.A branch of government accounting that records tax receipts

C.The exclusive study of probability axioms without any data

D.The science of collecting, organizing, presenting, analyzing, and interpreting data, covering both description of a dataset and inference to a population

Explanation: Statistics is defined by its full workflow: collect, organize, present, analyze, and interpret numerical (and categorical) data. Its scope includes descriptive summaries of the observed set and inferential statements about a larger population, which is why sampling, probability, and tests appear later in the same paper.

2Number of registered live births in an upazila in a month is which type of variable?

A.Nominal qualitative with no numeric meaning

B.Ordinal rank that cannot be counted

C.Continuous quantitative

D.Discrete quantitative

Explanation: Live births take isolated integer values 0, 1, 2, … and arise from counting, so the variable is discrete quantitative. Continuous variables can, in principle, take any value in an interval (height, time, yield).

3A table classifies households only as rural or urban. This classification of data is:

A.Chronological

B.Quantitative by class interval

C.Geographical by administrative district

D.Qualitative (categorical) by attribute

Explanation: Rural/urban is an attribute (a named category), so the grouping is qualitative classification. Quantitative classification uses numeric class intervals; chronological uses time; geographical uses place names such as districts or divisions.

4How does a histogram differ from a simple bar diagram used for categorical counts?

A.A histogram may only be drawn with horizontal bars

B.A histogram cannot display frequencies, only relative frequencies

C.Bar diagrams are reserved for continuous variables and histograms for names

D.Histogram bars for adjacent continuous classes touch, because the axis is a real-number scale

Explanation: A histogram represents a continuous (or class-interval) variable: class widths sit on a numeric axis and neighbouring bars touch. A simple bar diagram for categories leaves gaps, because the categories are not a continuous scale.

5A pie chart is the most appropriate diagram when the purpose is to:

A.Show how a total is divided into component shares

B.Show month-to-month trend in a long time series

C.Show the linear association between two quantitative variables

D.Show a frequency distribution with many unequal continuous classes

Explanation: A pie chart partitions 360° in proportion to each component's share of a single total, so it is built for composition. Trends, scatter, and detailed continuous distributions need line graphs, scatterplots, and histograms (or frequency polygons) respectively.

6On a less-than ogive, cumulative frequency is plotted against:

A.Class mid-points

B.Lower class boundaries

C.Upper class boundaries

D.Class frequencies (not cumulative)

Explanation: A less-than ogive graphs less-than cumulative frequency against the upper boundary of each class, because that cumulative total is the count of observations below that upper boundary. A more-than ogive uses lower boundaries.

7A frequency distribution is best described as:

A.A diagram that must use a circular layout

B.A listing of every raw observation in the order collected

C.A table that groups observations into classes and reports how many fall in each class

D.A formula that converts a sample mean into a z-score

Explanation: Grouping raw data into mutually exclusive classes and recording the class frequencies is the definition of a frequency distribution. It is a table (which may then be graphed); it is not the raw list, a z formula, or a pie layout.

8Which practice follows the usual rules for forming a frequency distribution of a continuous variable?

A.Classes that overlap so that a boundary value can be counted in two classes

B.Classes that are mutually exclusive, collectively exhaustive, and preferably of equal width

C.Leaving large unused gaps between consecutive class intervals on the scale

D.Using only open-ended first and last classes even when the range is known

Explanation: Standard construction uses non-overlapping (mutually exclusive) classes that cover the full range (exhaustive), usually with equal width so frequencies are comparable. Open ends and overlaps create ambiguity for the mean, median, and graphs.

9In a sample of 60 rice plots, 12 plots fall in the 4.0–4.9 t/ha class. What is that class's relative frequency?

A.0.12

B.12

C.0.20

D.5

Explanation: Relative frequency is class frequency divided by sample size: 12/60 = 0.20 (or 20%). It is a proportion, not the raw count 12 and not the reciprocal 60/12 = 5.

10The intersection of a less-than ogive and a more-than ogive drawn on the same axes estimates the:

A.Mode

B.Arithmetic mean

C.Range

D.Median

Explanation: At the median, half the observations lie below and half above, so the less-than and more-than cumulative curves meet at that value. The mode is read from a histogram (or by formula); the mean is a moment, not this intersection.

About the BCS Written Statistics Exam

BCS Written Post-Related Statistics (Subject Code 981) is a 200-mark descriptive paper in the Bangladesh Civil Service written examination conducted by BPSC. The official syllabus splits the paper equally: Part I (data, averages, dispersion, correlation, demography, index numbers, time series, sampling) and Part II (probability, distributions, sampling distributions, hypothesis testing, ANOVA, experimental design). It is sat by technical/professional cadre and dual-cadre applicants as the 200-mark post-related subject inside the 900-mark written stage. Official answers are written workings, not multiple choice. This free bank is an English-language MCQ study adaptation of that syllabus—not an official translation, format simulation, or substitute for practising full written solutions.

Assessment

Official assessment is a 200-mark descriptive written paper (Statistics, Subject Code 981) in two parts of 100 marks each. Part I covers descriptive statistics, demography, index numbers, time series, and sampling. Part II covers probability, distributions, sampling distributions, hypothesis testing, ANOVA, and experimental designs. Technical/professional cadre candidates (and dual-cadre applicants) sit this post-related paper as part of the 900-mark written stage. This bank is an English-language MCQ study adaptation, not an official translation, format simulation, or substitute for written computational practice.

Time Limit

4 hours is the duration used for BPSC 200-mark written papers on this site and in longstanding BPSC sitting practice; confirm the current routine

Passing Score

50% aggregate on the 900-mark written examination (BPSC page); per-paper minima also apply as set by BPSC

Exam Fee

Tk. 200 general (50th BCS); Tk. 50 for ethnic minority, persons with disabilities, and third gender; no separate written fee. Confirm the live circular. (Bangladesh Public Service Commission (BPSC))

BCS Written Statistics Exam Content Outline

10% of this bank (Part I of 100 marks)

Part I: Data, grouping, and presentation

Definition and scope of statistics, classification, types of variables, diagrams, frequency distributions, relative frequencies, and graphical presentation of grouped data.

15% of this bank (Part I of 100 marks)

Part I: Center, dispersion, and shape

AM, median, mode, GM, HM (raw and grouped), measures of dispersion, interpretation of SD, Chebyshev and normal rules, CV, skewness, and kurtosis.

8% of this bank (Part I of 100 marks)

Part I: Regression and correlation

Simple linear regression, least-squares estimates, correlation and rank correlation, correlation ratio, partial and multiple correlation, and R².

13% of this bank (Part I of 100 marks)

Part I: Demography, index numbers, and time series

CBR, CDR, fertility rates, TFR, migration, nuptiality, index-number properties, Laspeyres, Paasche, Fisher, and time-series components (trend, seasonal, cyclical, irregular).

4% of this bank (Part I of 100 marks)

Part I: Sampling designs

Population and sample, probability versus non-probability sampling, SRS, stratified, systematic and cluster sampling, sampling and non-sampling error, and sample size.

13% of this bank (Part II of 100 marks)

Part II: Probability and rules

Approaches to probability, addition and complement rules, joint and marginal probabilities, multiplication and conditional probability, and Bayes' theorem.

10% of this bank (Part II of 100 marks)

Part II: Random variables and distributions

Discrete random variables, binomial, hypergeometric, Poisson, and normal probabilities, means, and variances.

8% of this bank (Part II of 100 marks)

Part II: Sampling distributions and confidence intervals

Sampling distribution of the mean and proportion, CLT, confidence intervals for μ and p, and sample size for estimating a mean or proportion.

9% of this bank (Part II of 100 marks)

Part II: Hypothesis testing

H0/H1, Type I and Type II errors, significance level, one- and two-tailed tests, and z, t, F, and χ² procedures including two-sample and paired t.

10% of this bank (Part II of 100 marks)

Part II: ANOVA and experimental designs

One-way and two-way ANOVA, tests of correlation, multiple comparison, and the principles and layouts of CRD, RCBD, and Latin square.

How to Pass the BCS Written Statistics Exam

What You Need to Know

Passing score: 50% aggregate on the 900-mark written examination (BPSC page); per-paper minima also apply as set by BPSC
Assessment: Official assessment is a 200-mark descriptive written paper (Statistics, Subject Code 981) in two parts of 100 marks each. Part I covers descriptive statistics, demography, index numbers, time series, and sampling. Part II covers probability, distributions, sampling distributions, hypothesis testing, ANOVA, and experimental designs. Technical/professional cadre candidates (and dual-cadre applicants) sit this post-related paper as part of the 900-mark written stage. This bank is an English-language MCQ study adaptation, not an official translation, format simulation, or substitute for written computational practice.
Time limit: 4 hours is the duration used for BPSC 200-mark written papers on this site and in longstanding BPSC sitting practice; confirm the current routine
Exam fee: Tk. 200 general (50th BCS); Tk. 50 for ethnic minority, persons with disabilities, and third gender; no separate written fee. Confirm the live circular.

Keys to Passing

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

BCS Written Statistics Study Tips from Top Performers

1Weight revision equally to Part I and Part II (100 marks each). Do not skip ANOVA/design or demography because they sit at the ends of the syllabus.

2Practise full written workings for mean, variance, grouped median/mode, least squares, Laspeyres/Paasche/Fisher, binomial/normal probabilities, confidence intervals, t-tests, and ANOVA tables—the official paper is descriptive.

3Memorise when to use AM vs GM vs HM, Chebyshev vs the empirical rule, and SRS vs stratified vs cluster, then attach a one-line reason you could write in an essay.

4For inference, always state H0/H1, the test statistic family (z/t/F/χ²), and the rejection region before computing.

5Use this MCQ bank to lock concepts and arithmetic, then write past-style long answers under a 4-hour clock.

Frequently Asked Questions

What is BCS Written Post-Related Statistics?

It is Subject Code 981 in the BPSC BCS written syllabus: a 200-mark post-related paper (Part I 100 marks, Part II 100 marks) for technical/professional cadre and dual-cadre applicants. Topics run from descriptive statistics through probability, inference, ANOVA, and experimental design.

Is the official Statistics paper multiple choice?

No. The official paper is descriptive (written computational and long-answer work). This bank is an English-language MCQ study adaptation of the published syllabus, not an official translation, format simulation, or substitute for writing full solutions.

How many questions are on the official Statistics paper?

BPSC does not publish a fixed item count for this 200-mark written paper. Use the official Part I / Part II syllabus (100 marks each) rather than any practice-bank length.

How long is the BCS written Statistics paper?

4 hours is the duration used for BPSC 200-mark written papers on this site and in longstanding BPSC sitting practice. Always confirm the sitting routine and admit card for your cycle.

What is the pass mark?

The BPSC page requires 50% aggregate on the 900-mark written examination. Per-paper minima also apply as set by BPSC. Preliminary marks are not added to written+viva merit.

Is there a separate fee for the written Statistics paper?

No. For the 50th BCS, reporting citing PSC lists Tk. 200 for general candidates and Tk. 50 for ethnic minority, persons with disabilities, and third-gender applicants, paid via Teletalk. That application fee covers the cycle; confirm the live circular.

Who sits the post-related Statistics paper?

Technical/professional cadre candidates sit a 200-mark post-related subject instead of the extra general-cadre papers. Dual-cadre applicants sit the extra 200-mark post-related paper in addition to the general written set. Confirm posts in your circular.

In what language is this practice bank?

The bank is an original English-language MCQ study adaptation. Official BPSC materials may use Bangla and English; this is not an official translation or a simulation of the written-language environment.

100+ Free BCS Written Statistics Practice Questions

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