Chapter 1: Definition of Statistics, Importance & Limitations & Data Collection, Classification & Tabulation (CAIIB – Paper 1)
1. Which of the following best defines Statistics in banking?
A. Only collection of numerical data
B. Mere tabulation of facts
C. Science of collecting, classifying, presenting, analyzing and interpreting numerical data
D. Forecasting future without use of data
Statistics is not limited to data collection; it involves the entire process from collection to interpretation to help in decision-making.
2. One of the key importance of Statistics in banking is:
A. Assisting in policy formulation and forecasting
B. Avoiding decision-making
C. Eliminating the need for data collection
D. Creating mathematical puzzles
Statistics helps banks in decision-making, forecasting future business, and formulating sound policies.
3. Which of the following is NOT a function of Statistics?
A. Simplification of complex data
B. Promoting personal bias in interpretation
C. Assisting in comparison of data
D. Facilitating policy decisions
A limitation of statistics is that it may be misused to support bias, but its true function is objectivity. Hence, "promoting bias" is not a function.
4. The first step in statistical investigation is:
A. Tabulation of data
B. Classification of data
C. Presentation of data
D. Collection of data
Any statistical analysis begins with data collection, followed by classification, tabulation, and interpretation.
5. A limitation of Statistics is that:
A. It always gives precise answers
B. It never requires interpretation
C. It may be misused and does not reveal the entire truth
D. It replaces logical reasoning completely
Statistics is a tool that depends on proper use. It can be misused and shows only a partial picture, hence is considered to have limitations.
6. Which of the following is a major limitation of Statistics?
A. It deals only with aggregates and not with individual cases
B. It provides absolute truth in all situations
C. It eliminates the need for logical reasoning
D. It works without data
Statistics deals with mass data and does not analyze individual cases. Hence, it gives a general picture but not details of individuals.
7. Which of the following is NOT a demerit of Statistics?
A. It can be misused easily
B. It does not reveal the entire truth
C. It always works without any data
D. It ignores qualitative aspects
Statistics cannot work without data; this option is incorrect. Other listed points are real limitations of statistics.
8. According to Horace Secrist, Statistics may be defined as:
A. The art of forecasting future without data
B. The aggregate of facts, affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy
C. A collection of random guesses
D. The science of promoting personal bias
Horace Secrist defined statistics in terms of aggregates, numerical expression, and reasonable standards of accuracy.
9. Which statement best reflects a limitation of Statistics?
A. It deals with qualitative characteristics
B. It reveals the complete truth of all situations
C. It can work without logical interpretation
D. It does not study qualitative aspects like honesty or intelligence
Statistics is restricted to quantitative information; it does not measure qualities such as honesty, efficiency, or intelligence directly.
10. Which of the following correctly describes the scope of Statistics?
A. Limited only to mathematical puzzles
B. Restricted to data collection only
C. Science of collecting, classifying, presenting, analyzing and interpreting data for decision-making
D. Tool for expressing personal opinions
Statistics has a wide scope: from collection to interpretation of data. It is essential for objective decision-making in banking and business.
11. Data collected directly from respondents for the first time is known as:
A. Primary Data
B. Secondary Data
C. Derived Data
D. Classified Data
Primary data is original data collected firsthand through surveys, interviews, or observations for a specific purpose.
12. Which of the following is an example of Secondary Data?
A. Responses collected through a customer satisfaction survey
B. Direct interviews with branch managers
C. RBI publications and annual reports
D. Focus group discussions
Secondary data is already published or collected by others (e.g., RBI reports, government statistics, industry surveys).
13. Classification of data based on income levels (e.g., Low, Middle, High income groups) is an example of:
A. Temporal Classification
B. Geographical Classification
C. Qualitative Classification
D. Quantitative Classification
When data is grouped according to measurable characteristics like income or age, it is called quantitative classification.
14. The process of arranging data in rows and columns is called:
A. Classification
B. Tabulation
C. Graphical Representation
D. Sampling
Tabulation refers to the systematic arrangement of data in rows and columns for easy analysis and interpretation.
15. A good statistical table must have:
A. Decorative formatting and complex structure
B. Maximum number of rows and columns
C. Clear title, proper headings, units of measurement, and consistency
D. Data arranged without any sequence
A good statistical table should be simple, clear, properly titled, and systematically arranged with correct units and consistency.
16. A frequency distribution is primarily used for:
A. Collecting raw data
B. Organizing data into classes to show how often values occur
C. Predicting future business trends
D. Eliminating the need for classification
A frequency distribution organizes raw data into classes (intervals) and shows the number of times values occur, making large data easier to interpret.
17. In a frequency distribution, the difference between the upper and lower values of a class interval is called:
A. Frequency
B. Cumulative Total
C. Class Midpoint
D. Class Width
The class width (or size) is the difference between the upper and lower boundaries of a class interval.
18. The midpoint of a class interval in frequency distribution is obtained by:
A. (Lower class limit + Upper class limit) ÷ 2
B. (Frequency ÷ Class width)
C. (Upper class limit − Lower class limit)
D. (Cumulative frequency ÷ Total observations)
The class midpoint (or class mark) is calculated by taking the average of the lower and upper class limits.
19. In a cumulative frequency distribution, frequencies are:
A. Divided by class width
B. Multiplied by midpoints
C. Added successively across classes
D. Randomly arranged
Cumulative frequency is obtained by successive addition of frequencies from the first class to the last.
20. If the frequency distribution of income shows most values concentrated at the lower end with a long tail towards higher income, the distribution is:
A. Symmetrical
B. Positively Kurtic
C. Negatively Skewed
D. Positively Skewed
Income distributions usually have positive skewness – most people earn lower incomes while fewer earn very high incomes, creating a long right-hand tail.
21. A bar diagram is most suitable for representing:
A. Continuous frequency distribution
B. Discrete data such as number of customers by branch
C. Data requiring cumulative totals
D. Skewed frequency distribution
Bar diagrams are best used for discrete or categorical data like number of accounts by branch, types of deposits, etc.
22. Which graphical method is most appropriate to represent a continuous frequency distribution?
A. Bar Diagram
B. Pie Chart
C. Line Graph
D. Histogram
A histogram is best suited for continuous frequency distributions as class intervals are represented by adjacent rectangles.
23. In a Pie Chart, the angle for each sector is proportional to:
A. Class width
B. Class midpoint
C. Frequency of the class
D. Cumulative frequency
In a pie chart, each sector’s angle is proportional to the frequency. Angle = (Class frequency ÷ Total frequency) × 360°.
24. An Ogive is a graph of:
A. Cumulative frequency distribution
B. Relative frequency distribution
C. Frequency polygon
D. Discrete data distribution
An Ogive is a cumulative frequency curve, useful for locating median, quartiles, and percentiles graphically.
25. Which of the following statements about frequency polygon is correct?
A. It is constructed using vertical bars like a histogram
B. It cannot be drawn from a histogram
C. It represents discrete data only
D. It is obtained by joining the midpoints of histogram tops with straight lines
A frequency polygon is formed by joining the midpoints of histogram bars with straight lines, and helps compare two or more distributions.
26. The marks obtained by 10 students in a test are: 12, 18, 25, 20, 15, 30, 22, 18, 16, 24. What is the arithmetic mean?
A. 18.5
B. 20.0
C. 20.0
D. 21.5
Total = 200. Number of students = 10. Mean = 200 ÷ 10 = 20.0.
27. A frequency distribution of ages of 50 employees is given below. Find the modal class.
Ages (in years): 20–30, 30–40, 40–50, 50–60, 60–70
Frequency: 5, 12, 20, 8, 5
A. 30–40
B. 40–50
C. 50–60
D. 20–30
The modal class is the class with the highest frequency. Here, 40–50 has the maximum frequency (20).
28. For the following frequency distribution, find the median class.
Class: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 6, 10, 12, 8, 4
A. 20–30
B. 10–20
C. 30–40
D. 40–50
N = 40. Median class = class containing N/2 = 20th item. Cumulative frequencies: 6, 16, 28, ... So, 20th item lies in 20–30. Hence, median class = 20–30.
29. The daily wages of 100 workers are tabulated below. Find the class interval width.
Wages: 0–100, 100–200, 200–300, 300–400, 400–500
A. 50
B. 200
C. 150
D. 100
Each class = Upper limit – Lower limit = 100 (e.g., 0–100, 100–200, etc.).
30. The marks of 40 students are classified as below. Find the cumulative frequency of the class 40–60.
Marks: 0–20, 20–40, 40–60, 60–80, 80–100
Frequency: 4, 6, 15, 10, 5
A. 10
B. 15
C. 25
D. 30
Cumulative frequency up to class 40–60 = 4 + 6 + 15 = 25.
31. The marks of students are: 12, 18, 25, 30, 10, 28. What is the range?
A. 15
B. 10
C. 20
D. 25
Range = Highest value – Lowest value = 30 – 10 = 20.
32. The daily wages of workers (in ₹) are: 120, 150, 200, 250, 300, 180. Find the range.
