A bank 'xyz' wants to know about its popularity among the residents of a city 'ABC' on the basis of number of

Exercises · Q3

Q. A bank 'xyz' wants to know about its popularity among the residents of a city 'ABC' on the basis of number of bank accounts each family has and the average monthly account balance of each person. Briefly describe the steps to be taken for collecting data and what results can be checked through processing of the collected data.

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Concept understanding — Set Operations

Relational Algebra Operations: A First Look

Think of a relational database as a collection of neat, rectangular tables. Each table has rows (records) and columns (attributes). Now, suppose you want to ask questions of this data — "Which customers live in Delhi?" or "Show me all orders placed last month." Relational algebra is the set of basic operations you use to answer such questions. It is the language of queries at the most fundamental level.

You do not need to write code or do math. You only need to understand what each operation does to a table — like a set of tools in a toolbox.

The Core Operations

There are eight classic operations. They fall into two groups: those that work on one table at a time, and those that combine two tables.

Operations on a Single Table

Select (also called Restrict) — This operation picks certain rows from a table based on a condition. For example, from a table of students, you might select only those rows where the city is "Mumbai". The result is a smaller table with the same columns but fewer rows.

Project — This operation picks certain columns from a table. For example, from a student table with columns Roll No, Name, City, and Marks, you might project only Name and City. The result is a table with fewer columns. Duplicate rows are automatically removed.

Rename — This operation simply gives a new name to the resulting table or to its columns. It is useful when you need to refer to the same table more than once in a query, or when you want clearer column headings.

Note

Select and Project are the two most frequently used operations. Select narrows down rows; Project narrows down columns. Together they let you extract exactly the slice of data you need.

Operations That Combine Two Tables

Union — This combines two tables that have the same structure (same number of columns and compatible data types). The result contains all rows that appear in either table, with duplicates removed. Think of it as "add the rows of one table to the rows of another, but keep only unique ones."

Set Difference — This gives you rows that are in the first table but not in the second. For example, "Which students are enrolled in Course A but not in Course B?"

Intersection — This gives you rows that appear in both tables. For example, "Which customers have bought both a laptop and a printer?"

Cartesian Product — This pairs every row of the first table with every row of the second table. If the first table has 10 rows and the second has 5, the result has 50 rows. This operation is rarely used alone — it is the foundation for the most powerful operation of all.

Join — This is the heart of relational algebra. A join combines rows from two tables based on a related column between them. For example, you have a Customers table and an Orders table. The join operation matches each order to the customer who placed it, using the Customer ID column that appears in both tables. The result is a single table with all the customer details alongside their orders.

Important

The Join operation is what makes relational databases relational. Without it, data in separate tables would remain isolated. Joins let you connect information across tables — customers to orders, students to courses, products to suppliers — and answer questions that span multiple pieces of data.

Why Relational Algebra Matters

You will never write relational algebra directly in a real database system. Instead, you will use a language like SQL (Structured Query Language). But relational algebra is the underlying logic that every SQL query follows. When you write SELECT ... FROM ... WHERE ..., you are really performing a sequence of Select, Project, and Join operations behind the scenes.

Understanding relational algebra gives you a clear mental model of what a query actually does. It helps you reason about whether your query is correct, whether it will return the right rows, and how to break a complex question into simple steps.

Tip

When you face a tricky query question, think in terms of relational algebra first: "Which tables do I need? Which columns? What condition connects them?" Then translate that into SQL. This approach rarely fails.

A Simple Example to Fix the Idea

Imagine two tables:

Students — columns: Roll No, Name, City

Courses — columns: Course ID, Course Name, Roll No (the student enrolled)

You want: "Names of students from Delhi who are enrolled in the course 'Database'."

Here is how relational algebra would break it down:

Select from Students where City = "Delhi" → a temporary table of Delhi students.
Select from Courses where Course Name = "Database" → a temporary table of that course.
Join these two temporary tables on Roll No → a table with Delhi students enrolled in Database.
Project only the Name column → your final answer.

Each step is simple. Together they answer a meaningful question.

Relational algebra is not about computation. It is about thinking in tables — how to slice, combine, and reshape them to get the information you need. Once you see data as tables and queries as operations on those tables, the whole subject becomes intuitive.

This is a plain theory question — it asks for a brief description of data-collection steps and the results that can be checked through processing.

Steps for collecting data

First, the bank must define its target population: every family residing in city ABC. Since surveying every family is impractical, the bank should use random sampling — selecting a representative subset of families so that the results can be generalised to the whole city.

The data to be collected from each sampled family is:

Number of bank accounts the family holds (across all banks, or specifically at bank xyz — the question implies accounts in general, but the bank's interest is in its own popularity, so it would likely ask about accounts held at xyz).
Average monthly account balance for each person in the family (again, presumably at bank xyz).

This data can be gathered through a structured questionnaire (physical or digital) or by directly accessing the bank's own customer database for those families who are already customers. For non-customers, a door-to-door survey or telephonic interview would be needed.

The collected data must be cleaned — removing incomplete or inconsistent entries — and then coded into a structured format (e.g., a spreadsheet or database table) for analysis.

Results that can be checked through processing

Once the data is processed, the bank can compute several meaningful statistics:

Average number of accounts per family in city ABC. A low average suggests low penetration; a high average suggests many families already use the bank.
Distribution of account balances — the mean, median, and range of average monthly balances per person. This tells the bank whether its customers are mostly low-balance or high-balance account holders.
Correlation between number of accounts per family and average balance per person. For example, do families with more accounts also tend to have higher balances? This can guide product bundling strategies.
Market share estimate: the proportion of families in the sample that hold at least one account at bank xyz. This directly answers the question of popularity.
Geographic or demographic patterns (if location or occupation data is also collected) — e.g., which neighbourhoods have the highest account-holding rate.

The key insight: the bank is not just counting accounts — it is measuring depth of relationship (accounts per family) and financial engagement (average balance), both of which together give a far richer picture of popularity than a simple headcount.

✓Final answer

The bank should collect data through random sampling of families in city ABC, recording the number of bank accounts per family and the average monthly balance per person; processing this data yields estimates of average accounts per family, balance distributions, correlation between the two, and the bank's market share — all of which together measure its true popularity.

The bank must first define its target population (families in city ABC), then collect data through a survey or census on the number of accounts per family and average monthly balance per person, and finally process this data using statistical measures (mean, median, mode, range, standard deviation) and visualizations (histograms, bar charts) to understand account distribution and balance patterns.

This is a plain theory question — it asks you to describe the steps for data collection and the results that can be obtained from processing that data. There is no code, no MCQ, no case study. The answer should be structured as clear explanatory paragraphs.

The Idea: Data Collection and Processing as a Two-Phase Process

Data collection and data processing are two sides of the same coin. Collection is about gathering raw facts; processing is about extracting meaning from them. For the bank 'xyz', the goal is to understand how many accounts families hold and what their average balances are — this tells the bank about its market penetration and the financial health of its customers.

Phase 1: Data Collection Steps

Step 1: Define the target population.

The bank must clearly specify that the target is all families residing in city 'ABC'. A "family" needs an operational definition — for example, a group of people living together and sharing a common kitchen. This avoids ambiguity.

Step 2: Choose the data collection method.

Two main options exist:

Census: Collect data from every family in the city. This gives perfect accuracy but is expensive and time-consuming.
Sample survey: Select a representative subset of families (using random sampling, stratified sampling by locality, etc.). This is more practical for a large city.

Step 3: Design the data collection instrument.

A questionnaire or interview schedule should capture:

Family identifier (to avoid duplication)
Number of bank accounts held by the family (across all banks, or specifically at 'xyz'? The question says "number of bank accounts each family has" — likely all accounts, but the bank may want to distinguish its own accounts)
For each person in the family, the average monthly account balance (over, say, the last 6 months)

Step 4: Pilot test the instrument.

Test the questionnaire on a small group to catch confusing questions, missing options, or data entry errors.

Step 5: Train the data collectors.

Ensure field staff understand how to ask questions neutrally and record responses accurately.

Step 6: Execute the data collection.

Deploy the survey, monitor progress, and handle non-response (families that refuse or are unreachable).

Step 7: Validate and clean the data.

Check for inconsistencies — for example, a family reporting 10 accounts but zero balance, or a person's balance being negative. Remove or correct such records.

Phase 2: Processing and Results

Once the raw data is collected, the bank can process it to answer specific questions. Here are the key results that can be checked:

Result 1: Distribution of number of accounts per family.

Calculate the mean (average accounts per family), median (the middle value), and mode (most common number of accounts).
A histogram showing the frequency of families with 1, 2, 3, … accounts reveals whether most families have a single account or multiple accounts.
If the mean is close to 1, the bank has low penetration; if it's higher, families are using multiple banks.

Result 2: Distribution of average monthly balances per person.

Compute the mean balance, median balance, and standard deviation (spread).
A histogram of balances (grouped into ranges like ₹0–₹1000, ₹1000–₹5000, etc.) shows the financial profile of residents.
The bank can identify what proportion of people have very low balances (potential churn risk) versus high balances (potential for premium services).

Result 3: Relationship between number of accounts and average balance.

A scatter plot with "number of accounts per family" on the x-axis and "average balance per person" on the y-axis can reveal patterns.
For example, families with more accounts might have higher average balances (wealthier families diversify), or the opposite (people open multiple accounts to keep small balances in each).

Result 4: Comparison across localities or demographics.

If the data includes locality or age group, the bank can compute averages per zone. This helps decide where to open new branches or target marketing.

Result 5: Identification of outliers.

Families with an unusually high number of accounts (say, 10+) or extremely high balances might be businesses or high-net-worth individuals — the bank can follow up for relationship management.

Watch out

A common mistake is to confuse data collection with data processing. Collection is about gathering raw facts (e.g., "Family X has 3 accounts, person Y has ₹12,000 average balance"). Processing is about summarizing and analyzing those facts (e.g., "The average number of accounts per family is 2.1"). The question asks for both steps — do not skip either phase.

Tip

For a real-world bank, the most actionable result is often the correlation between account count and balance. If families with more accounts also have higher balances, the bank might launch a "consolidate your accounts" campaign to attract those balances. If the correlation is negative, the bank needs to improve its service to retain customers who spread their money across banks.

✓Final answer

The steps for data collection are: define the target population (families in city ABC), choose a census or sample survey method, design a questionnaire capturing number of accounts per family and average monthly balance per person, pilot test, train collectors, execute the survey, and validate/clean the data. The results from processing include: distribution of accounts per family (mean, median, mode, histogram), distribution of balances per person (mean, median, standard deviation, histogram), relationship between account count and balance (scatter plot), locality-wise comparisons, and identification of outliers.

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The Idea: Data Collection and Processing as a Two-Phase Process

Phase 1: Data Collection Steps

Phase 2: Processing and Results

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