Tables, Matrices and Structured Data Short Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Tables, Matrices and Structured Data short notes for CAT: 4 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Summary: The 5-Step Master Algorithm

Summary

5-Step Master Algorithm

1. Translate

Convert every mean, median, mode, min, and max into hard numerical constraints (

Sum = Mean \times Count

2. Map

Draw the matrix. Write the row sums and column sums on the borders.

3. Fix

Place the absolute values first (Min, Max, and Mode).

4. Split

Use the Median to lock the middle value and divide the remaining slots.

5. Distribute

Allocate the remaining sum to the empty slots, using extreme values (maximize/minimize) to satisfy all conditions.

Summary: The Composition Checklist

Summary

The Composition Checklist

Check the Base

Is it per 100g? Do the columns sum to 100? (Look for the "Other" balancing category).

Map the Clues

Convert text (ratios, differences) into algebraic variables.

Use the Anchor

Use the sum equation (

Sum = 100

) to solve for the variables.

For Mixtures

Use weighted averages based on total weights, never simple averages of percentages.

The Grid Matrix Checklist

Translate Averages to Sums

$C e l l S u m = n \times A v er a g e$

Exploit the Magic Grid

$R o w T a r g e t = C o l T a r g e t = G r an d T o t a l / n$

Bound the Cell Sums

$n \times min \leq C e l l S u m \leq n \times ma x$

Leverage Distinctness

If averages are distinct, find the exact set of $n^{2}$ integers.

Partition and Map

Group the cell sums to match the Row/Column targets.

Resolve Sub-items

Use parity, odd/even checks, and remaining ranges to fill the final items.

The Longitudinal Data Checklist

Track the Surviving Cohort

$P_{s t a r t} (Y e a r X) = P_{s t a r t} (Y e a r X - 1) - D e a t h s (Y e a r X - 1)$

Verify the Mortality Rate Denominator

Check if it's per initial cohort or surviving population.

Cumulative vs Incremental

$Incremental = Cumulative (C u r r e n t) - Cumulative (P r e v i o u s)$

Map the Pandemic Grid

Draw Days $\times$ Neighbourhoods. Write row and column sums explicitly.

Use the Deficit Method

$Deficit = (Cells \times Max Value) - Actual Sum$

Tables, Matrices and Structured Data: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Data Interpretation and Logical Reasoning MCQ

In a restaurant rating matrix, if the summary statistics state that the "modal rating" for a specific worker is 4, what does this definitively mean?

A.
The rating of 4 was given to this worker more frequently than any other rating.
B.
The worker received a rating of 4 from every single restaurant.
C.
The middle rating when all ratings are sorted is 4.
D.
The difference between the highest and lowest rating is 4.

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct definition check for "Mode" in the context of rating data, recognisable because it asks for the meaning of a specific summary statistic.

Step 1: Recall the definition of Mode.

The mode is the value that appears most frequently in a dataset.

Step 2: Apply to the context.

A "modal rating" of 4 means the number 4 appears more times than 1, 2, 3, or 5 in that worker's set of ratings.

Step 3: Evaluate the options.

Option A matches the definition of mode perfectly. Option B describes a constant rating, Option C describes the median, and Option D describes the range.

Answer: A

Question 2 · Data Interpretation and Logical Reasoning MCQ

In a grid matrix, a specific box contains $n$ sub-items. If the average value of these sub-items is $A$ , which of the following formulas correctly calculates the total sum of the sub-items in that box?

A.
$A + n$
B.
$A - n$
C.
$A im es n$
D.
$A / n$

Correct Answer:

Step-by-Step Solution

Key idea: This is a foundational translation question, recognisable because it asks for the mathematical relationship between a cell's average, its count, and its total sum.

Step 1: Recall the definition of an average.

$Average = \frac{Total Sum}{Count}$

Step 2: Rearrange the formula to solve for the Total Sum.

$Total Sum = Average \times Count$

Step 3: Substitute the given variables.

$Total Sum = A \times n$

Answer: C

More short notes in this unit

chapter

Tables, Matrices and Structured Data Short Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Tables, Matrices and Structured Data short notes for CAT: 4 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

A question from this chapter

Question 1

In a restaurant rating matrix, if the summary statistics state that the "modal rating" for a specific worker is 4, what does this definitively mean?

Question 2

In a grid matrix, a specific box contains n sub-items. If the average value of these sub-items is A, which of the following formulas correctly calculates the total sum of the sub-items in that box?

Free preview ends here

Login to view the complete short notes

Creating an account is free. You get the rest of this chapter, step-by-step solutions, and a study plan built around the topics you are actually weak at.

Why MastersUp

Personalised first. High quality throughout.

Most platforms hand everyone the same content. Here the content moves with your performance, topic by topic.

Built around you, not around a syllabus PDF

Every answer you give moves your topic-level intelligence rate. The next question, the next revision card and tomorrow's plan all change with it.

Revision that hits your weak spots

We only revise topics you have actually attempted and are still below the safe bar on — never the same chapter on repeat.

Questions calibrated to the real exam

Each question carries a measured toughness. You are served a rung above your current level, so practice keeps stretching you.

Notes written for recall, not for volume

Full lesson cards for first study, curated short-note cards for the last mile — with derivations, traps and exam patterns marked.

One place for everything

Notes, chapter practice, previous-year questions, test series and full-length papers — all feeding one picture of your preparation.

Honest progress

No vanity streaks. Progress here means chapters mastered and accuracy that held up on harder questions.

Unlock the whole course

Full notes and short notes, the complete question bank with worked solutions, mock tests, full-length papers, and an adaptive plan that rebuilds itself as you improve.

View all plans Start free