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৪৯তম বিসিএস ⎯ পরিসংখ্যান [৯৮১]

পরীক্ষা৪৯তম বিসিএস ⎯ পরিসংখ্যান [৯৮১]তারিখতারিখ অনির্ধারিতসময়21 minutes২৮ বৈধ · ১ অসম্পূর্ণ
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Exam - 01 Topics: Introduction to Statistics: Definition and scope, Variables. Presentation of Data: Charts or Diagrams, Types of diagrams. Grouping Data: Frequency Distribution, Graphical presentation of frequency distribution, quartiles. Measures of Central Tendency: MEAN (AM,GM,HM), MEDIAN, MODE [Source: Class - 01 and Relevant Books]
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৪৯তম বিসিএস ⎯ পরিসংখ্যান [৯৮১]

৪৯তম বিসিএস ⎯ পরিসংখ্যান [৯৮১] · তারিখ অনির্ধারিত · ২৯ প্রশ্ন

১.
Which of the following is not true for Statistics?
  1. ক
    Statistics are aggregate of facts.
  2. খ
    The science of collecting, organizing, analyzing, interpreting, and presenting data
  3. গ
    All numerical statements of facts are statistics, but all statistics are not numerical statements of facts.
  4. ঘ
    Statistics are collected for a predetermined purpose
ব্যাখ্যা

Explanation: Statistics is specifically concerned with data — how to collect it, organize it, analyze it, interpret results, and present findings for decision-making. Moreover, single and isolated figures are not statistics for the simple reason that such figures are unrelated and cannot be compared. For example, the age of a student is 20. This is not statistics. But if we consider the age of student1=22, student2=23, student3=21, this is statistics. Besides, the purpose of collecting data must be decided in advance. But, “C) All numerical statements of facts are statistics but all statistics are not numerical statements of facts”- is false. Correct statement should be-
“All numerical statements of facts are not statistics, but all statistics are numerical statements of facts”. For example, “Textile industries are growing” is not statistics. “Number of Textile industries increased from 250 in 2005 to 350 in 2015” is statistics. So, statistics must be numerical. But isolated numerical number (The age of only 1 student) is not statistics.

Source: a) Business Statistics, S.P. Gupta, M.P. Gupta. b) Live MCQ Class lecture

২.
Which is NOT a characteristic of statistics?
  1. ক
    Helps in predictive analysis
  2. খ
    Summarizes large data
  3. গ
    Directly measures emotions like happiness
  4. ঘ
    Informed decision-making
ব্যাখ্যা

Explanation: Statistics helps summarize data, make predictions, and support decisions. But it cannot directly measure subjective internal states (like “happiness”) with absolute precision. You can approximate emotions via surveys (Likert scales) or proxy measures (behavioral indicators), but that is indirect and subject to measurement error and interpretation—so C is not a true “importance” of statistics. A, B, and D are genuine applications

Source: a) Business Statistics, Md. Abdul Aziz. b) Live MCQ Class lecture.

৩.
Which of the following is a limitation of statistics?
  1. ক
    Purposive misuses.
  2. খ
    Statistics rules are mutable.
  3. গ
    Statistics gives only an overall measure
  4. ঘ
    All of the above.
ব্যাখ্যা
Explanation:
Statistics helps summarize data, make predictions, and support decisions. But it cannot measure an individual’s condition, rather gives a trend. The average mark of a class is 60. This does not tell the condition of an individual student. Statistical numbers can be misused. For previous example, one teacher can say that his class is doing fine. But most of the students might get less than 30 and average number might be 50 because some exceptional students got more than 90. Moreover, statistics fit model and “all models are wrong, some models are useful”- Box. The rules vary based on dataset. 

Source: a) Business Statistics, Md. Abdul Aziz. b) George E.P. Box c) Live MCQ Class lecture.
৪.
A population that can be counted completely is called:
  1. ক
    Infinite population
  2. খ
    Finite population
  3. গ
    Sample
  4. ঘ
    Continuous population
ব্যাখ্যা

Explanation: A finite population has a countable number of members (e.g., all books in a library, all students in a university). An infinite population (coin flips, theoretical outcomes) cannot be fully enumerated. A sample is a subset, not the whole population. “Continuous population” is not standard terminology in this sense.

Source: a) Business Statistics, Md. Abdul Aziz. b) Basic Statistics, B.L. Agarwal.

৫.
Which of the following is a qualitative variable?
  1. ক
    Height of a person
  2. খ
    Blood type
  3. গ
    Number of books in a library
  4. ঘ
    Weight of an object
ব্যাখ্যা

Explanation: Blood type is categorical (qualitative) because it describes a quality or characteristic without numeric measurement.

Source: a) Business Statistics, Md. Abdul Aziz. 

৬.
Which scale of measurement does “I.Q. score” represent?
  1. ক
    Nominal
  2. খ
    Ordinal
  3. গ
    Interval
  4. ঘ
    Ratio
ব্যাখ্যা

Explanation: I.Q. score has equal intervals but no true zero (Zero I.Q. score does not mean absence of any intelligence), so it’s interval scale.

৭.
“Family size” is an example of:
  1. ক
    Continuous variable
  2. খ
    Discrete variable
  3. গ
    Interval variable
  4. ঘ
    Qualitative variable
ব্যাখ্যা

Explanation: Discrete variables take countable whole numbers without fractions (e.g., 20 students, 5 members of a family). 

Source: a) Business Statistics, Md. Abdul Aziz. b) Basic Statistics, B.L. Agarwal

৮.
Which chart is best suited to show percentages of a whole when series are divided into a large number of components?
  1. ক
    Bar chart
  2. খ
    Histogram
  3. গ
    Pie chart
  4. ঘ
    Frequency polygon
ব্যাখ্যা

Answer: A
Explanation: A pie chart divides a whole into slices whose sizes are proportional to percentages or parts of the whole, making it intuitive for showing composition (e.g., budget shares). Be cautious: pie charts can be hard to read when there are many categories or similar slice sizes—bar charts may be better for comparison.

Source: a) Business Statistics, S.P. Gupta, M.P. Gupta.

৯.
Which of the following is false for histogram:
  1. ক
    Bars have gaps between them
  2. খ
    Modes can be determined from histogram
  3. গ
    Bars touch each other
  4. ঘ
    Both A,B are false.
ব্যাখ্যা

Explanation: Histograms show continuous data, so bars touch to indicate no gap between intervals. Graphically, the modes of the data can be determined by histogram.

Source: a) Business Statistics, Md. Abdul Aziz. 

১০.
Which graphical tool uses midpoints of histogram bars?
  1. ক
    Ogive
  2. খ
    Pie chart
  3. গ
    Frequency polygon
  4. ঘ
    Stem-and-leaf plot
ব্যাখ্যা

Explanation: A frequency polygon is formed by plotting the class midpoints on the x-axis and connecting consecutive points with straight lines. It’s essentially a line version of a histogram that emphasises shape and trend.

Source: a) Business Statistics, Md. Abdul Aziz. b) Live MCQ class lecture

১১.
Which is true for Q1?
  1. ক
    10% of data below this point
  2. খ
    It is equal to 25th percentile
  3. গ
    50% of data below this point
  4. ঘ
    It is equal to median.
ব্যাখ্যা

Explanation: Q1 (lower quartile) is the value below which 25% of data falls. 25th percentile also tells us same thing.

Source: Mathspace, Statistics Libre Texts, Business Statistics, Md. Abdul Aziz. 

১২.
Which measure of central tendency is most affected by extreme values?
  1. ক
    Mean
  2. খ
    Median
  3. গ
    Mode
  4. ঘ
    Quartile
ব্যাখ্যা

Explanation: The arithmetic mean uses every value in the dataset and sums them. A single very large or very small value (an outlier) can pull the mean substantially.

Example: dataset [2, 3, 4, 5, 100] → mean = (2+3+4+5+100)/5 = 114/5 = 22.8, which is far from the “center” of the lower four numbers. The median (middle value) would be 4, which is not affected by the 100 as much.

Source: a) Basic Statistics, B.L. Agarwal b) Live MCQ class lecture

১৩.
Harmonic mean is used mainly when averaging:
  1. ক
    Salaries
  2. খ
    Rates such as speed
  3. গ
    Heights
  4. ঘ
    Weights
ব্যাখ্যা

Explanation: The harmonic mean is appropriate for averaging rates when the quantity being averaged is defined per unit (e.g., speed over equal distances). If you travel the same distance twice at different speeds, the correct average speed is the harmonic mean, not arithmetic mean.

Source: a) Statistics, Freedman, Pisani, Purves b) Business Statistics, Md. Abdul Aziz

১৪.
Which of the following is an example of continuous data?
  1. ক
    Number of goals scored in a match
  2. খ
    Shoe size
  3. গ
    Temperature
  4. ঘ
    Number of cars in a garage
ব্যাখ্যা

Explanation: Continuous variables can take any value within a range, including decimals (e.g., 36.5°C, 36.51°C). Number of goals or cars are discrete (countable whole numbers). Shoe size is often treated as discrete or ordinal depending on measurement system.

Source: a) Business Statistics, Md. Abdul Aziz. b) Live MCQ class lecture

১৫.
Which diagram best represents frequency distribution of continuous data?
  1. ক
    Pie chart
  2. খ
    Histogram
  3. গ
    Bar chart
  4. ঘ
    Line graph
ব্যাখ্যা

Explanation: Histograms are specifically for continuous data and frequency distribution. But, histogram can be quite misleading if the distribution has unequal class intervals. Moreover, we cannot contruct a histogram for distributions with open-end class.

Source: a) Business Statistics, S.P. Gupta, M.P. Gupta. b) Live MCQ class lecture.

১৬.
In a stem-and-leaf plot, the “stem” represents:
  1. ক
    The last digit
  2. খ
    The leading digit(s)
  3. গ
    The frequency
  4. ঘ
    The midpoint of class intervals
ব্যাখ্যা

Explanation: A stem-and-leaf plot shows each data value split into a stem (leading part) and leaf (final digit). Example dataset: 12, 14, 17, 21, 23 → Stem | Leaf
1 | 2 4 7
2 | 1 3
Here stems are the tens (1, 2) and leaves are unit digits (2,4,7...). This preserves raw data while showing distribution.

Source: a) Business Statistics, Md. Abdul Aziz.

১৭.
A cyclist travels 40 km at 20 km/h and then another 40 km at 40 km/h.
Find the average speed.
  1. ক
    30 km/h
  2. খ
    26.67 km/h
  3. গ
    40km/h
  4. ঘ
    None of above
ব্যাখ্যা

Explanation: Formula of Harmonic mean will be used here because distance is same and speed unequal.

Solution: The Harmonic Mean (HM) formula is:

For n numbers x1,x2,x3,…,xn: 

HM= n/(1/x1+1/x2…)

So, HM= 2/(1/20+1/40)=2/(0.05+0.025)=2/0.075=26.67km/h

১৮.
Monthly incomes (in $) of 8 workers are:
2000, 2200, 2400, 2600, 2800, 3400,3000, 3200. Find Q3 using the formula:
  1. ক
    4.5
  2. খ
    5.5
  3. গ
    6.5
  4. ঘ
    None of the above.
ব্যাখ্যা

Explanation:
First, we have to rearrange the number in ascending order.
we get,
2000, 2200, 2400, 2600, 2800, 3000, 3200, 3400. 

Now, Qk = k(n+1)/4

So, Q3 = 3(8+1)/4=27/4=6.75. So, Q3 is between 6th and 7th value.

 Q3 = 3000 + 0.75 × (3200 − 3000) = 3000 + 150 = 3150

১৯.
Find geometric mean of the numbers 2, 4, 8.
  1. ক
    2
  2. খ
    4
  3. গ
    6
  4. ঘ
    None of above
ব্যাখ্যা

Explanation: GM= (x1×x2×x3….xn)(1/n)

Here, GM = (2 × 4 × 8)^(1/3) = 64(1/3) = 4

২০.
If AM=15, and GM=12 for two positive numbers, what is the value of HM?
  1. ক
    9.6
  2. খ
    8
  3. গ
    9.4
  4. ঘ
    9.2
ব্যাখ্যা

Explanation:
For two positive numbers we know:

AM × HM=(GM)2

So, HM = ((GM)2)/AM
= 144/15
= 9.6

২১.
The mean height of 50 men is 175 cm, and the mean height of 70 women is 165 cm. What is the combined mean height?
  1. ক
    169.16 cm
  2. খ
    169.6 cm
  3. গ
    170 cm
  4. ঘ
    170.6 cm
ব্যাখ্যা

Explanation:
Combined mean= (50 × 175 + 70 × 165)/(50 + 70)
= 20300/120
=169.16

২২.
In a grouped distribution, the modal class is 20–30 with frequency 25. The class before it has frequency 18, and the class after has frequency 15. Class width = 10. Find Mode.
  1. ক
    25.2
  2. খ
    25.6
  3. গ
    26
  4. ঘ
    26.4
অনির্ধারিত
ব্যাখ্যা
অপশনে সঠিক উত্তর না থাকায় প্রশ্নটি বাতিল করা হয়েছে। 
​
২৩.
Data: 4, 7, 8, 10, 12, 15, 18, 20, 25, 28. Find the IQR.
  1. ক
    10
  2. খ
    15
  3. গ
    14
  4. ঘ
    12
ব্যাখ্যা

Explanation:
Q1 = median of lower half = median of (4, 7, 8, 10, 12) = 8
Q3 = median of upper half = median of (15, 18, 20, 25, 28) = 20
IQR = Q3 - Q1 = 20 - 8 = 12

২৪.
If the mean is greater than the median, the distribution is:
  1. ক
    Symmetrical
  2. খ
    Negatively skewed
  3. গ
    Positively skewed
  4. ঘ
    Uniform
ব্যাখ্যা

Explanation:
In a positively skewed distribution:
Mean > Median > Mode.
The tail extends toward higher values.

২৫.
Marks: 12, 18, 20, 25, 28, 30, 32, 35. What is the median?
  1. ক
    25.5
  2. খ
    26.5
  3. গ
    27.0
  4. ঘ
    28.5
ব্যাখ্যা

Explanation

Median = middle value(s) when data is sorted.
Here, n = 8 (even)
→ median = average of 4th and 5th values: (25 + 28) ÷ 2 = 26.5

২৬.
An investment grows by 15%, 10%, and 20% over 3 years. Find the average annual growth rate.
  1. ক
    14.98%
  2. খ
    15.00%
  3. গ
    14.50%
  4. ঘ
    14.20%
ব্যাখ্যা

Solution:
Factors: 1.15 × 1.10 × 1.20 = 1.518
Cube root: (1.518)1/3≈1.1498
Growth rate = 14.98%

২৭.
The ages of 5 players are 20, 22, 25, 27, 30. What is the mean age?
  1. ক
    25
  2. খ
    24.5
  3. গ
    24.8
  4. ঘ
    23
ব্যাখ্যা

Solution:
Sum = 20 + 22 + 25 + 27 + 30 = 124
Mean = 124 ÷ 5 = 24.8

২৮.
The ages of 5 players are 20, 22, 25, 27, 30. What is the mode age?
  1. ক
    25
  2. খ
    24.8
  3. গ
    24
  4. ঘ
    No Mode
ব্যাখ্যা

Explanation: There is no repetition of numbers. So, Mode is not present.

২৯.
Liton Das scores 30, 25, 23, 27, 21. What is the median?
  1. ক
    No median
  2. খ
    23
  3. গ
    25
  4. ঘ
    Both a, c can be right based on the situation.
ব্যাখ্যা

Explanation: We rearrange the dataset: 21, 23,25,27,30. Median is the middle data. So median = 25